Solid hardwood should not be installed below grade. However, engineered hardwood can be installed in basements as long as you do not have an existing moisture problem.
There are several carpet fibers on the market that will essentially oxidize any organic liquid that comes in contact with the carpet. Additionally, and perhaps more importantly, there is padding that is designed with pets in mind that prevents liquid from reaching the decking.
Compared to other products, you may find that tile and grout require less maintenance than other floors, but it is not maintenance free. Grout should be sealed and caulking needs to be maintained to prevent deterioration of the backer board.