In Fallout: New Vegas for the PS3, Xbox 360, and PC, there are a couple ways to exploit glitches for an unlimited amount of XP.
Note that these very well may be patched in the future, so if you plan to use them then I would suggest waiting to run any patches it tries to download for you.
1. Old Ben’s Escort Glitch
There is a man named Old Ben sitting by a fire near The King’s Headquarters in Freeside. With a speech skill of 50 or higher you can persuade Old Ben to offer his escort services to the local bar. Successfully completing the speech challenge will net you 61 xp. Follow Old Ben back from the bar after he’s done and wait until he sits down and you can do the speech challenge again for unlimited xp. You can find Old Ben sitting by a fire close to The King’s headquarters in Freeside.
2. Sergeant Bitter-Root’s Name Glitch
With a  speech skill of 30 or higher and being neutral or friendly with NCR, head to Camp McCarran and look for Sergeant Bitter-Root in one of the tents. Ask him about his name and there will be an option for a 30 speech skill level attempt. Keep selecting “Bitter-Root. You have an unusual name.” then ask to talk about something else, and the name option will keep coming back.
3. Vault 11 Download Glitch
Travel to Vault 11 and you will get a quest to find out what has happened there. Continue the quest until you get the overseer’s passcode and enter it into the computer. Next you will be led to the Sacrificial Chamber. Use a Stealthboy to sneak by everyone there. A door will open on the left as you walk in. Go in and access the computer mainframe. You will be given one “Override” option and two “Download” options. Select the second download option to get 500 XP. Instead of exiting the mainframe, keep selecting the second download option to receive 500 XP every time.
4. Aurelius of Phoenix’s Barter Glitch
With a barter skill of 35 or higher, head to Cottonwood Cove. Look for a man named Aurelius of Phoenix and talk to him. Choose the option to barter with his camp for ammunition and supplies, which will net you 35 XP. You can keep repeating that option as many times as you want.
5. Gambling for XP
If you have a lot of money to spend and want some XP, then play roulette. You’ll get 100 XP even if you lose.