I LOVE Asiago and always use it for spaghetti. It's pretty interchangeable with parmesan, but I think it has a fuller flavor.
Another thing I like doing with it: heat up a non-stick pan. Put about a half cup of shredded Asiago into the pan, and spread it a bit into a circle. Cook until it's golden on the bottom, then flip over and cook until golden. Remove and cool. Nice, crispy treats that are good for appetizers, too.