It's a classic, but just in case you haven't heard... use white wine to get out red wine stains.
Just a short time soaking (or with water dripped on) makes lots of crud easier to wipe-up.
Rub fabric softener on your shower tiles after cleaning them. It makes more water run off, so you'll get less mildew or residue. (The Bounce brand was recommended. I haven't tried this one yet.)
Cream of tartar (see Potassium tartrate) is great for removing tea stains and some rust stains. According to the Wikipedia article, it's also good for cleaning coins. It's nice to use for cleaning food containers like tea pots, because it can be used in food (like meringues and baking powder), so you don't have to worry about leaving trace amounts.