Chicken certainly, yes. Corn would be better roasted in the oven in the husk. Peel back the husk, add some butter and squeeze it back together. The grill pan is also good for seafood such as shrimp or lobster. Split in half or butterfly and cook in the shell right on the grid. Steaklike fish is also very good. You'll get some nice pan seared marks. I wouldn't worry about the smoke detector, but cranking up a ceiling fan is a good idea.

I live in an apartment in Manhattan, so no grill for me, either. Generally, a grillpan can be used for anything that ought to go on an outdoor grill, but sometimes you need to make an adjustment or two. Anything that gets really smokey (like one of my favorite chicken dishes, done in a mustard/honey/veg oil marinade) isn't a great idea, unless you disconnect your smoke detector first. And then there's the fact of having less surface area to work with, and no built-in lid. So I probably wouldn't grill pizza on the stovetop. But veggies, absolutely. Meat, fish, chicken, for sure. Fruit, too (peaches--amazing). Grilled cheese sandwiches are great, and prettier than in a regular skillet.