A new storage system was implemented in 2008 for your ground and flying mounts. They now no longer take up bag or bank space. You now "learn" each mount, once you get them, similar to a spell. You can carry all of your mounts around at once and summon them whenever you want. The same system is used for companion pets.
Press "Shift-P" to open up your pet menu. You will then see a list of all of the pets you have. Right click on any of your existing pets to store them. If you want to summon a pet more quickly, drag the icon to one of your action bars.