Ninja Gaiden is an absolute must-try. While Black is the preferred version since it is the most feature complete and balanced version, the original goes for like $10 if you're on a budget and aside from an inferior camera there isn't much that a first time player is gonna notice and miss when it comes to OG versus Black. If you're modding the system or just have the cash to shell out for Black def spring for that, but if you're tight on cash the OG release is still a phenomenal game.
Panzer Dragoon Orta is as good as the rail shooter entries ever got imo. I recognize the brilliance of Zwei, but Orta not only includes a good port of the original but also features some of the most awe inspiring setpieces you'll find on the Xbox.
Halo CE and Halo 2 are no-brainers and dirt cheap. Not even sure I need to explain these. They're timeless classics and well worth anyone's weekend on top of being cheap. If you have a friend to co-op with, even better!
If you're into cars, definitely check out Project Gotham Racing 2. Forza 1 is a fantastic sim-style game on the system but for a more arcadey and laid back game that still has tons of content and depth, PGR2 is a fantastic game. Plus you get a playable version of Geometry Wars in the garage, 2 games in 1 :D
Crimson Skies is a super dope combat flight game. Super easy to pick up and play with some of the best visuals in its genre in a very underappreciated era of aerial combat. Playing in an alternate 1930s as a sort of rogueish sky pirate crew is a ton of fun!
Phantom Dust is a mix between a JRPG, an action platformer and a card game and it fucking RULES! Amazing art direction, captivating story and entirely unique combat system make it a must-play.
Final big recommendation is Breakdown. It's a highly ambitious first person action game by Namco where the gimmick is that it has very in depth movement, beat-em-up combat AND shooter gameplay but the game never leaves first person. you just gotta see it to really get it. The story is a bit silly but also pretty wild and fun to follow. Like Phantom Dust, you'll never play another game like it. Outrun 2 and Outrun 2006 are amazing if you dig Outrun in any capacity, same goes for Crazy Taxi 3.
Jet Set Radio Future is obviously fantastic and a pretty fun weekend play, usually comes as a double pack with Sega GT 2002 which is a pretty solid attempt at replicating Gran Turismo. Even if you plan on playing Forza, Sega GT 2002 is worth an afternoon or two.
Gunvalkyrie is another great game as mentioned by several peeps already. If you like Fromsoft the Otogi duology is well worth a look, its arguably their best work that entire console generation. Mechassault 1 and 2 are super fun and arcadey mech games. Fast paced but still carry that heft and sense of weight that Mechwarrior was known for.
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@sijaab said, removing the clock capacitor is also super duper easy and necessary to ensure the long-term health of your system. If you have a 1.6 model don't do it, but if you do have a 1.5 or prior system you should definitely do it or look into having someone do it for you at some point. Again, it is way easier than you might think though, don't be afraid!
