From Diablo Wiki
The Paragon Levels system is an end game feature. These levels are accessed once a character reaches the maximum level of 60. Once a character reaches level 60, experience gained from monster kills, quests, destructibles, kill spree bonuses or any other source counts towards the Paragon levels.
There are 100 paragon levels, and each level up rewards a character with the same attribute bonuses as a normal level up (3 to the class main stat, 2 vitality, 1 to the other two stats), plus a passive bonus of 3% to Magic Find and Gold Find.
As of v1.08 Paragon levels are bonuses solely to the character who earns them, though the developers have suggested that Paragon bonuses might go to the account in the future. They've also suggested that some character customization might be enabled by Paragon levels.
In mid-2013 the developers began suggesting some future changes to the Paragon Levels system.
One main question fans always ask is what will happen to Paragon Levels in the Expansion. It's widely-assumed the cap will increase from 100, but it's not clear what bonus that would provide, with Magic Find and Gold Find already maxed out at the 300% hard cap at Paragon 100. Perhaps the MF/GF cap would be increased? 
We've definitely talked about things like taking Paragon and decoupling it from your character specifically and making it something that is more account-over working. So that any time you invest in the game is rewarded and you don’t feel like we’re taking anything away from you if you want to try new characters or try out different play styles within the game. That’s something we've looked into a lot.
Also, maybe potentially adding some sort of customization within the paragon system. Sort of in the vein of a throwback at a Diablo II start location. We've looked at things like that. We definitely have plans to flesh it our more in time. We don’t need to design it from the ground up. What it does, it does well, and we just need to make it more encompassing.
You've also mentioned that you’re not looking into increasing the cap of Paragon. It’s going to be a hundred for at least a while, right?
Travis Day: For the foreseeable future. I think at some point you can expect the cap to go up. The cap isn't even really there to necessarily make an end point to the player. The intent was for paragon 100 to take a long time to get to. Which it does. But as we improve different aspects of the game (make changes to Monster Power, Monster Density, etc.) the time that it takes players to fill out that cap is shorter than we’d like. And once you do cap out, it definitely removes a very important reward for you – your XP stops going up. So that’s something that we want to address – at some point we’ll definitely look at that cap.
About those customizations to the paragon system – what about the people who are already capped? Will they be receiving any kind of reward on patch day?
Travis Day: Yes, absolutely. If we’re making the sweeping changes to the Paragon, the people who invested time will certainly have the reward that is associated with that investment.
No changes to the Paragon system are expected before the Diablo 3 Expansion, sometime in 2014 or later. More details should be revealed before the launch.
Official Paragon Level Details
- After a player reaches level 60, killing monsters and completing combat challenge streaks (Killing Blow, Massacre, etc) will begin to award experience towards Paragon levels
- There are 100 Paragon levels
- Every Paragon level will reward you with:
- Core stats such as Strength, Dexterity, Intelligence, and Vitality in amounts similar to what you’d gain from a normal level
- 3% Magic Find and 3% Gold Find
- In addition, a distinctive border will surround your character portrait in the in-game party frame to denote your Paragon progression, with a new frame earned after every ten levels. Your Paragon level will also be visible to other players wherever your normal level is shown.
- Nephalem Valor now grants +15% Bonus Experience per stack, as well as +15% to Magic Find and Gold Find
- Magic Find will now cap at 300% (Nephalem Valor bonuses, Fortune shrines, and multiplayer bonuses will stack beyond this cap).
- Magic Find is no longer averaged among all players in a multiplayer game.
Paragon Levels Experience
Players quickly datamined the patch for precise details about the experience gains required for Paragon Levels. Most players can advance through the first 10 or 15 Paragon levels fairly quickly, but the progress slows down in the 20s and 30s, and then grows markedly slow past level 40. Above level 80 further advances become more of a grind.
Though the total experience needed is considerable, it was just two weeks before the first character reached Paragon level 100. The winner was a Barbarian named Alkaizer, who dinged to the top on September 6, 2012 and became famous by giving his name to the popular Act Three experience farming Alkaizer run.l
Initially, characters into the Paragon levels did not gain experience from quest rewards or other bonuses besides monster killing. (Experience shrines didn't even spawn in Inferno at that point.) Subsequent patches enabled these missing features, and added any more ways to gain rapid experience with more gear bonuses, bigger bonuses from multiplayer games, and more.
The page here and information in the tables and chart is obsolete, paragon levels are now uncapped
Huge table showing current and cumulative experience required for all 100 Paragon levels. Level 50 requires 2.1 billion experience and is just over 20% of the way to Paragon 100. The actual halfway point comes around level 78.5, when a character has earned 5.2 billion of the 10.4 billion experience required for P100.
- For Levels 1-60, experience requirements increase at a rate of 1,440,000/level.
- For Levels 61-70, experience requirements increase at a rate of 2,880,000/level (=2*1,440,000).
- For Levels 71-80, experience requirements increase at a rate of 5,020,000/level (=3.5*1,440,000).
- For Levels 81-90, experience requirements increase at a rate of 6,480,000/level (=4.5*1,440,000).
- For Levels 91-100, experience requirements increase at a rate of 8,640,000/level (=6*1,440,000).
| Experience points
(needed for level)
| Experience points total
(from level 0)
| Other stats
| Magic and Gold|
* * Table courtesy of Diablo.kalais.net.
A handy pie chart giving a proportional view of the total Paragon Level experience gain. The amount per level increases steadily from 1-59, and then increases more steeply at levels 60, 70, 80, and 90.
Several screenshots showing off aspect of the Paragon system.