All kinds! Italian, of course, is number one, but lately I've been on an "All-American" frenzy. You know, what they call "comfort food." I also really love all kinds of Latino food, especially Cuban!
Well, here are a few places I can suggest:
Italian - Carmine's - My wife and I go to a few Italian restaurants but our favorite lately has been Carmine's.
Comfort Food - Mike Ditka's - Get your burgers, steaks, pork chops, sandwiches here.
Greek - In the western part of downtown Chicago, you'll find Greek Town and my favorite restaurant there is Costa's Greek Dining & Bar. It's kind of pricey compared to the other restaurants in the area, but I feel Costa's food is the best. It's a bit prosaic for me to say, but you should try the gyros.
Late Night Food - In the heart of Lincoln Park, you'll find the The Weiner's Circle. The place is a bit of a dive and you don't go there expecting service (actually, they're known for their comically rude service), but the place is famous for college and late night partyers. Get your Chicago-style hot dogs here.
Pizza - I know I've had this discussion with my East Coast bretheren, but I have to defend my hometurf here - you have to try Chicago-style pizza. It's a meal all by itself and you don't have to scrape off the layer of grease that comes with the New York-style pizza.
In truth, I'm not a big fan of pizza in general so I'm just joking with you East Coasters (just to let you know before you get your panties in a bunch ). With that said, I do find the pizza at Giordano's tasty. If you're ever in Chicago, you have to have the deep dish. Why, I don't know? That's what people around here always say.
Cuban - Cafe 28 - I'm also a big fan of Cuban food. There are a couple of places that are a bit more "authentic" (read: less trendy) than Cafe 28, but they aren't in the best part of town so I wouldn't suggest tourists going there.
Tapas - Cafe Iberico - If you like tapas/latin food, you can't go wrong with Iberico. Cheap sangria too.