Most of the good anime offered through a video store is often found in the children s section. There, you will find wonderful works by directors like Hayao Miyazaki. My Neighbor Totoro and Kiki s Delivery Service are two of his more well known works. This type of animation is slowly becoming more available for rental, but currently is still quite rare. When all else fails most anime can be bought at movie and record shops.
Stocks usually vary greatly between different retailers so it pays to look around a little.
You should be wary though. Anime is offered in both dubbed and subtitled formats. More often than not I have found the dubbing on most series to be badly acted. The problem with this is that it takes away from the total impact of a story. This is especially true with more intense dramas.