If you have interest in the arcade titles on the Xbox 360, and follow the advice above about Trials, try getting the Arcade Compilation 3 Pack Microsoft offers. It has Trials HD, Limbo and 'Splosion Man on disc, and can be found frequently for $10 online (which is usually the standard price for each game if bought individually from the Xbox Marketplace) from places like NewEgg and Amazon.
They're 3 distinct games, but a fairly grand in style and scope for mere arcade titles. Plus, there are demos for each game online, so you can try them for free to see if they appeal to you.
And if you have interest in games like Fable, where you get to explore, try looking at the Mass Effect Series. There's demos available for 2 and 3, which are both very different from the first game, so look at videos on YouTube to see if you'd enjoy how they play. EA recently released a Mass Effect Trilogy bundle, but it lacks the downloadable content for each of the games (and there's a lot of it for each which adds lots of extra playable content for the stories). The bundle is $60 now, but if you follow this site there's bound to be a deal on it soon enough.
And if you get into the Gears of War series, keep in mind that it has 2 player cooperative play in both 1 and 2, via either online or split-screen, so you can play the full game with someone else if you're interested. If you're looking to play with others, the Halo games (3, ODST, Reach, Anniversary and 4) have the ability to be played in cooperative throughout the campaign, too, so check out those.