From Diablo Wiki
The "end game" is a term used to describe the play style, game features, and player behavior engaged in by expert players with high level characters.
At that point in the gaming experience, high level characters have completed all of the quests and other challenges, and players are no longer entertained simply by grinding through the normal game. Players want greater challenges at that point, and many turn to item finding, PvP dueling, or other non-traditional occupations.
Many game designers end up producing most post-release content for the end game, since that's where most players are spending their time, rather than simply making new level 1 characters and going through the whole experience again. The, added to Diablo II in the v1.11 patch, is a good example of added end game material, since it was only available on the realms, and only possible to engage in with very high level, well-equipped characters.
- See the End Game category for numerous Diablo III news items related to this issue.
Max Clvl 60 Announcement
Diablo III's end game debate changed radically in September 2010, when the developers revealed that the maximum level characters could achieve in the game would be 60, rather than 99 (or 100) as they'd previously hinted. 
- Bashiok: The 60 level cap we’re working with came from a lot of time and thinking about our content and how we want the experience to feel at every level. It so happens that it works for us really well.
- Of course it all comes down to an XP curve. We could, for instance, say the level cap in Diablo III is 60 and then pace that curve and gain out over what we estimate it took someone to reach 99 in Diablo II. Of course we wouldn’t do that but it should help illustrate that the time from 1-60 in Diablo II does not equal the amount of time it will take to reach 60 in Diablo III. 60 levels versus 99 levels doesn’t mean less content or less powerful characters, etc.
- The leveling experience is always going to stop somewhere because the real game is the item hunt. So, instead of letting it drag out to a less meaningful 80 or so levels like most people saw in Diablo II we have 60 levels of awesome; at every level you’ll get a meaningful and noticeable increase in power. It has a ton of other benefits and fixes a lot of problems a higher cap causes, but I’ll take pause.
The Leveling Curve
The number (60 vs 99) isn't the real issue, of course. It's just a number. What matters is how the content is balanced to the level progression, and that's where D3 makes a huge change. The design goal is that the levels match the amount of content; a character who finishes all three difficulty levels should be around level 60. Thus the end game becomes about finding items, PvP, reaching achievements, and creating new characters to do it all over again. This was first explained by Bashiok in September 2010. 
Additional posts made clear that the projected level up rate is something like 30/50/60 when finishing the Normal/Nightmare/Hell difficulties. This point was once again expounded upon in greater depth by Bashiok in August of 2011:
We don’t expect that people are going to play start to finish, Normal to Inferno, in one sitting. Because of that it implies replays of specific areas (as enemies/bosses respawn when you leave and start a new game) which adds in some guess work on XP gains. It may be that you need to stick around in Hell difficulty for a bit longer because you beat the game at level 58 or something, but it shouldn’t be a long drawn out XP farming situation just so you can advance – if we do it right.Again, personal play habits will influence leveling curves but we’ll do our best to make it smooth.
Though this is a big change, Blizzard's explanations for it have proven fairly convincing, and most fans are on board with the changes, or at least the design motivation behind them. A public vote on Diii.net demonstrated this, and in most comment threads about the issue, a majority of fans are supportive, or at least not full of angry objections.
It's universally-speculated, thought not yet confirmed, that the maximum level of characters will rise in the expansion packs. This is done in many RPGs, most noticeably in World of Warcraft which began with a max level of 60, then saw it rise to 70, 80, and 85 in the first three expansions.
End Game Goals and Philosophy
Blizzard has stated numerous times that their goal for the end game of Diablo III is to basically build on what worked in Diablo II, namely the item-hunting metagame (that could be argued as being the main game), and to fix what did not work in Diablo II's end game.
The main perceived problems, as addressed by Blizzard, are what they call "path of least resistance" runs where a player would find the most efficient route to a monster or boss that is known to have a very desirable loot table. The player then performs these item runs over and over until they receive what it is they want, even though it is tedious, boring, and not exactly the most exciting thing a player could be doing. However it is, of course, the most efficient way for a player to find reward in Diablo II.
So in lieu of this, Blizzard has implemented a fourth difficulty level named Inferno which makes ever monster one level about the clvl max, namely 61, across the entire difficulty. There are other tweaks, such as potential exclusive modifiers and also more aggressive and modified AI, to aid this.
There’s a couple ways we’re doing that, some of which we’re not talking about just yet.
Primarily it’s focused around Inferno and creating a consistent difficulty across the entire act. By having a flat difficulty across the entire game in Inferno it evens things out so that no matter where you want to go you’re being challenged, and you have a good chance at getting good drops. That’s intended to open the game up so there’s simply more freedom for the player to go anywhere in the game and have an equal chance at good drops.
There will probably still be a slight difficulty curve in Inferno, as enemies simply become more complex and have greater abilities later in the game, but we’re making an effort to make it as even across the board as possible. It’s something we’ll very likely have to keep tweaking after release.
In addition we’re attempting to de-emphasize path of least resistance by creating a more equal value across monster types. We’re not going to get into specifics about who can drop what or how much, but our intent is that being out in the world exploring should be as lucrative (potentially more) as simply aiming for the quickest-to-reach boss and running that over and over.Getting people out into the world of the game and away from repetitive boss runs is essentially our goal. It’s going to be tough because people will find a path of least resistance, and they will make that the game. We’re going to have to keep on top of it, and truthfully it’s something we’re still working on. We’ll likely want to have some additional features to support these ideals, but just getting Inferno tuned right is our current end-game goal for ship.
Plans Beyond Release
The Inferno difficulty mode is not the development team's plan for end game, but it may very well serve as a sort of gateway to introduce other methods and styles of play. The development team has plans to possibly introduce more facets of end game through content patches or other means. However, these plans are being closely guarded by Blizzard, and information on what will be contained in this content is as yet unknown.
PVP and Hardcore
Blizzcon 2009: 
- Jay Wilson: It’s definitely better if the players explore more of the game. It will be a lot more fun for them, but players will gravitate toward the route that is fastest for what they want. Even if that route makes them crazy… even if that route is not fun at all. It’s not their fault. It’s our fault as designers. It’s our job to make sure that the path of least resistance is also the path of most fun.
- We do have specific systems planned for the late game and our goal for those systems is to make sure that players are experiencing as much of the content over again as possible.
- The best example of where we feel we do this well in our other games, in World of Warcraft, is the quest system, which really gets you to move all over the world and do lots and lots of different things. The basic, core actions of the game are very repetitive. It’s not that they’re not fun, but the boredom with anything comes with repeating the same thing in the same way. If you could repeat the same thing in a different way it stays interesting a lot longer and that’s definitely going to be a goal for us.
Blizzcon 2009: 
- Jay Wilson: a player's tendency is to follow the path of least resistance. We learned this in World of Warcraft, if you make the fastest way to level killing boars until your eyes bleed, then that's what players will do. They won't do the most fun thing. They'll do what gets them progression the fastest. So we put in this massive quest system, it's a ton of work, but what it does is, it says, go kill some dudes over there, run over there, grab me three of those things, do this thing over here. When the player's always doing something different, the game stays fresh, it stays fun to play for a long time.
- This is the philosophy we've put into the Diablo endgame. So it's not that you're not doing runs, it's that you're not doing the same run over and over again. There's a reason for you to kill this boss, then that boss, then maybe explore that dungeon. There's a benefit that pushes you around through all the content. We have some systems planned for that, but that's definitely our focus, to get out of that…I'm doing one run over and over again, and get to the idea of, I'm doing every possible run that can be done. To show off the broadest array of content.
Bosses and end game variety, from Blizzcon 2009: 
- Julian Love: We're trying to have it so that there's more things to do than just, like, when you've played the game a ton, rather than just doing boss runs to get items, we want to have more things like quest runs or things like that, different challenges you can do to get the item drops we have. We want to vary up that late-game stuff for the super experienced guys.
Leonard Boyarsky interview, October 2009: 
- Hellforge: Yeah that was a huge problem in D2 where people did Bloody runs or Baal runs over and over.
- Leonard Boyarsky: Yeah, we have ideas about how we want to handle those things, specifically it’s something we’ve talked about at length and we have a solution that we think is gonna work really good and keep people from having to continually do the same runs over and over.
- I’m sorry for putting the idea down outright, but it’s not a very sexy solution to make the end game more interesting or exciting. Sort of just draws it out, or maybe resolves some pacing issues that existed in Diablo II, which was a different game.
- I’ve said this a lot but try not to think of Diablo III as an extension of Diablo II. Things like experience curves are not a constant that we have to take from Diablo II, implement directly into Diablo III, and then be really upset about it and have to try to solve the problems they give us. This is a new game being built from the ground up, problems aren’t inherited from the previous games. We can do whatever we want.
- Anyway, we have many ideas, there have been many good ideas discussed out there on how to solve some of the end game issues. Some of them are pretty much spot-on for ideas we’ll likely go ahead with. Most of that design and work on end-game hasn’t started yet though. We’re still working primarily on building out the core game experience (act-to-act world and dungeons and monsters). Just the basic play through on Normal. Which is coming along quite well still, I might add.
- I was in a meeting with Jay and Wyatt earlier (about something completely different), and Wyatt expressed specifically that giving players some sort of end-game that doesn’t involve grinding areas or bosses is something that keeps him up at night. It’s a real problem, and it needs a real solution. It’s also very much in the minds of our designers and something we will try to remedy as long as we need to.
- All that said, long-term end game concerns are I know a top priority of you regulars here and on our fansites, but there’s so much good stuff in the game that I really hope these WHAT IF scenarios don’t take away from the wow-factor of just enjoying what we have to share with you.
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