There are many. From the top of my head I personally love all of the GTA series, Saints Row series, Slender, Amnesia, Trouble in Terrorist Town, Skyrim, Fallout series, COD series, Dead Island series, Dead Rising series, Assasins Creed series, Prop Hunt. They're all fun :-)
DISNEY INFINITY! It's good for all ages! I mean, you're never to young for Disney, right? Not only can you play actual levels but there's also a thing called the toy box where you can build, basically, whatever you want! It's just amazing, it's mine craft meats Disney meets Skylanders! Brilliant! Brilliant! I understand if that's not really your thing. But it's certainly my thing! I love running around the streets of Metroville as Elastigirl, bashing up bad guys, kicking around and throwing citizens, smashing windows and driving my car into stuff. Of course, you don't have to do all that violent stuff I said I love doing (besides bashing up bad guys part), that's just what I like to do! I've done the M.U one, and it's good! Except for when I lost my TP gun, but I found it! I haven't done the POTC yet, or Cars or anything other ones yet! It's an awesome game and comes on a lot of consoles! But I'm not sure if it's on the PC and I hear the DS (every kind of DS they make it on) is absolutely crap! But yeah, I've got it on the Xbox360 Kinect and I LOOOOOOOOOOOVE it!
Fallout, fear, mercenaries, red faction, dead space, defiance, Jericho, killzone, last of us, orange box, crysis, resident evil, call of duties, any game with zombies, dead island, border lands, battle field,metro, star trek (the new one) rainbow six, wow, there are tons more.
It all comes down to preference and past experience. I find that games that are very similar to what I have played are much more fun, in the beginning, then ones that are complete different. But I love all games especially when they are challenging. Some people love more simple easy to play games, like Angry birds. I would say if there is a local gaming magazine in your area. Read it for game reviews and they should also include a disk with demos and or free games. If there is a local internet place you can game, go try the games that they have there to find what you like and what you don't like. Try Steam's store. They have allot of free games on there that you can try. And a small tip if your not going to play with friends online try to avoid it, unless you want to play competitively. Most online players are just a bunch of S"poo"T (self censoring is the key to unhappiness you know) heads.
Try this site. You pay any price for the games (even $1 if you're a cheap skate) and it supports charity. :) Good if you like indie games, but sometimes mainstream games also come on there (I got Battlefield 3 and Deadspace there once) https://www.humblebundle.com
I would recommend World of Warcraft , it's an awesome mmorpg while you're at it you can do join this private server,Eternal-WoW, is completely free has an awesome community , no lag , awesome Staff , and everything works perfectly. it offers 5 Wrath of the Lich King realms and 1 cataclysm 4.3.4 realm. If you make up your mind send me a message.
Pirate and wizard101 it's free forever and you can do some of the story but to continue the story you have to get a prepaid card or pay by credit card one month membership is 10$ so with a regular salary I don't think it would be too much money...then again I don't have a job yet so I wouldn't know for sure.
GTA Series are great! Especially San Andreas and th V ! I haven't played the V yet, but i have seen gameplay and it looks awesome! A great strategy game is Age of Mythology the Titans Expansion! it is an old one, but really amazing!!!