If the birthday in question falls during months with warm weather, consider holding the festivities at your local park. There's plenty of space for games and activities -- and zero worries about stained carpeting. You can make use of what's already in place, such as picnic shelters and playground equipment; check with your park district to see if you need any permits or reservations.
Of course, you'll want to have a back-up location planned in the event of inclement weather. Keep that location in mind when sending invitations, because you don't want to invite more kids than can comfortably celebrate in that more limited space.