Please note that this system will be pretty much outdated after Paragon 2.0 has been released. The strategies included for faster Paragon leveling will still be valid, but the original Paragon system only applied it's level to a single character on your account (hardcore or softcore),whereas the new system will be account-wide for hardcore or softcore characters on your account.
A character that has reached level 60 will not stop earning experience. Experience will now be applied to "Paragon Levels", which have a maximum of 100. (Paragon 2.0 will NOT have a maximum Paragon Level, and the bonus will be applied to your entire account.)
The first Paragon Level gives you a bonus portrait upgrade (for in-game multiplayer display of your character). After this, every 10th level gives you a new upgrade on your portrait.
Each Paragon Level also gives you a bonus +3% each to Magic Find and Gold Find. This bonus applies to your MF and GF cap (300%) with your equipped items and 1/5th of your follower's equipped item bonus.
Each Paragon Level will finally give you a +3 bonus to your primary attribute, +2 bonus to vitality, and +1 bonus each to the other two attributes.
Paragon Leveling Strategies
The fastest way to gain mass exp for Paragon Levels is to find your "sweet spot" .... the MP level at which you barely 1-hit everything in your path other than elite packs; spending no more than 10 - 15 seconds to clear those guys on average. You want to farm on Monster Power 1 as a minimum, in order to take advantage of the extra monster spawns added to acts 1, 2, and 4. Wherever you choose to farm can now be just as good as Act 3 alone used to be. See Paragon Farming Routes below.
To find your "sweet spot" ... start at Monster Power 1 and keep bumping up the monster power until you no longer 1-hit stuff ... then back it down a notch. Remember to back it off a bit further for multiplayer, as each player gives +50% base hp to the monsters (and you may no longer 1-hit them, thus unintentionally adding time to the overall run.
Paragon Farming Routes
In Act 1, the popular choice for Nephalem Valor stacks is Festering Woods. 1 - 3 elite packs in the upper area, with the possibility of an event, and 2 guaranteed bosses in the mini dungeons make this a very fast zone to run. To finish off for 5 NV stacks, Cathedral 3rd floor has a guaranteed elite pack, or you could hit Leoric's Manor. Some people go straight for the Fields of Misery + Keywarden instead. Next location to hit is Weeping Hollow and possibly the Halls of Agony 2nd floor... rinse and repeat.
Act 1 areas to NOT skip ... Festering Woods, Fields of Misery, Decaying Crypt (Fields of Misery dungeon), Weeping Hollow.
In Act 2, pick a starting spot to grab some quick elites to stack yourself up. Vault of the Assassins is a good choice, as is Black Canyon Mines + Alcarnus. After you have reached 5 Nephalem Valor, you hit Oasis + Keywarden, then Desolate Sands, and then the Storm Halls dungeon ... finish off with Zoltun Kulle if you like for the drops + quest bonus. (most dungeons you will just skip over)
Act 2 areas to NOT skip ... Flooded/Ancient Cave(oasis), Forgotten Ruins(Oasis - you get ZK's head here), Vault of the Assassin (5 - 11 elites!), Storm Halls (ZK's Nexus area - good monster density), Zoltun Kulle (quest)
In Act 3, hit wp for Arreat Crater 2 ... go BACKWARD into the tower and up to the previous waypoint (should get 4 - 6 elites along the way) ... if you're still short 1 or 2 Nephalem Valor stacks, jump to the wp in Tower 1 and clear that floor (should be 1-3 there) ... then go to Stonefort and clear to end + Keywarden, then The Keeps 2 and 3, and jump to Rakkis and clear back to the waypoint on the bridge including the mini-quests you find on the way (or vice versa), finish up with The Core + Azmodan for quest. (craters used to be awesome for exp, but the Stygian Crawlers got badly nerfed on exp ... still ok for drops and gold though!)
Act 3 areas to NOT skip ... Keeps 2nd floor(best monster density/exp in Act 3), Frost Cavern/Ice Cave(Battlefields - good drops down there!), Rakkis(mini-quests give great exp bonus), Azmodan (quest)
Act 4 is not recommended for those who wish to survive. The Keywarden uses Earthquake (8000% dps over 7 seconds) and the act overall is very short. For those who need the Infernal Machine plans, it is best to do it on as high a Monster Power as possible, so that you do NOT ever have to go back there again.
Act 4 areas to NOT skip ... Skip it all! >.<
Act 5 is not yet part of the game. It will be added in the Reaper of Souls expansion, and more information concerning possible new Paragon Leveling Routes will be forthcoming after release.