If you are talking about the $99 X360 it does exist.  But you have to pay $15 monthly for it.

Well it is hard to recommend people games when everybody has different preferences.  For me I use my X360 for Multiplayer games more than anything.  I do prefer XBL over PSN for example so games like CoD, BF, or even sports games I prefer on X360 because XBLG and the operating system.  Also I prefer the controller for X360.  As for exclusive content I can give a few games that I personally enjoyed.  

Halo, Gears, and Fable are the three most obvious ones although personally i wouldnt buy a console for fable.  

Forza hands down I would say is the best racing game if you are into racing.  Specially if you are artistic because you can make some awesome cars on that game.

Lost Odyssey for JRPG's.  People say it is what Final Fantasy XIII should have been.  

Ive also enjoyed Viva Pinata (Simulator)  BattleBlock Theater (Platformer) Aegis Wing (Space shooter) Minecraft ( if you dont have a PC)  Trials Evolution, mark of the Ninja, Dead or Alive 4, Project Gotham Racing, Alan Wake (one of my favs) and Left 4 Dead are all great games.  Of course a few of those are also for PC so it depends on that as well.  A lot of people seem to like Crackdown as well although personally i think it is just ok.  State of Decay right now is exploding on to the scene as well.

I mean it really comes down to what you like and what makes it worth it to you.  For me XBL is a selling point but not everybody may feel that way but if you want to play Gears and Halo (two of my all time favorite series) they really are fantastic games although a lot of that is because multiplayer so it also depends on if you are a multiplayer gamer.  I mean if you are a single player gamer I'd recommend the PS3 over the X360 as Ive enjoyed more singleplayer games on my PS3 than my X360.  So it does depend on what type of gamer you are even though Halo and gears still does have a good story.  A lot of xbox exclusives are revolved around multiplayer in some shape or form.

With all that said I wont tell you if you should buy it as it really comes down to your preferences and if you can justify the money for what you buy.