Infinite XP
Note: Using the "Infinite XP" glitches can leave you weak. The higher level you are, the more difficult the game gets. You will encounter more and stronger enemies, and they will have better weapons in better conditions.
Use the following trick to get 5 experience points each time it is performed. Go to Craterside Supply (found in Megaton) with a few frag mines (so you do not have to re-equip the mines). Go into the room behind the mercenary. Get close to the back side of the wall that the mercenary is leaning against, and place a mine. Quickly pick it up as it will immediately be armed and ticking. Repeat this as many times as desired.
Have a Speech skill of at least 30. Visit Big Town by travelling northwest from Springvale Elementary. Talk to Bittercup about her dating exploits. Talk with Pappy about how he came to Big Town with Bittercup to start a Speech challenge. If you fail, the challenge will still be available to retry. Repeat the challenge until you are successful. You will get six experience points, and the option to retry the challenge can still be selected. Repeat the challenge as many times as desired. Note: This requires the unpatched version of the game.
Be at least level 10, and have a 60 Sneak skill. Unlock the Mister Sandman perk. Go to the Smith's house at Andale. Sneak upstairs at night while everyone is sleeping. Try to pickpocket the boy, but instead select "Murder". You will not lose Karma and gain over 50 experience points. Because the boy does not actually die, you can repeat this as many times as desired. Note: The game may glitch and become unresponsive. Also, this requires the unpatched version of the game.