Jenni and I rented an apartment a few years ago when we took the boys to Ireland with us. I thought it was great and I highly recommend it as an alternative to staying in a hotel.
Lately I've been hearing more and more about house swapping. It's a pretty interesting concept and possibly a big cost saver to your travel budget. Your accommodations end up costing you nothing. To do it: you register with a service, post pictures of your home, and make arrangements with the owners to swap homes with them for a weekend or a couple weeks. I haven't done it myself, but something to consider.
This is a pretty good article from Travel + Leisure where the authors talk about their experience.
Special Report: House Swapping - Articles - Travel + Leisure