As soon as I could afford it, I made myself a Mechano-Hog, and that became my permanent ground mount in Dalaran and battlegrounds. I was tired of the loping stride of the animal mounts, and it was really fun to give friends and lowbies rides. For flying, I used the Azure Drake from Malygos from the moment I won it all the way until the Cataclysm starting quests.
After doing a few of the quests with my husband, we decided to use smaller mounts while we were leveling. The larger mounts blocked out more things on the ground and were more likely to cover up the quest givers when we were turning in quests. So he went from the Bronze Drake to a wyvern mount, and I decided to use my Headless Horseman's Mount. When we reached level 85, I considered switching back to a flashier flying mount -- the Green Proto-Drake, one of my carpets, one of the Netherwing Drakes ... I have quite a collection, but not yet a Mountain O'Mounts. I do like to show them off now and then, but the Horseman's mount has turned out to be very useful. It doesn't dismount you when you go underwater or inside a building where you can use a ground mount. I find this extremely handy when doing the Therazane daily quests because I don't have to choose a different mount when I enter or leave the cave with the crystal quests.
So how do you decide which mount you'll use? Do you show off your rarest mounts? Do you have a random mount addon? Do you switch it up, or use an old favorite?