Interrogation Droid

The Interrogation Droid vanity pet can be bought from the dark side vendor, Lord Davorak on the Imperial Fleet or Vindir on the Republic Fleet, for 25,000 credits.  They can be found in the Galactic Trade Market-section on the Imperial Fleet. You have to be at least level 3 dark to be able to buy it.

Once out it looks like this:

Minimech CE

The Minimech CE is a mouse droid which comes with the purchase of a Star Wars: the old republic collector's edition.

Once out it looks like this:

Mouse Droid

The Mouse Droid can be bought from Toth, the Security Key Vendor on the Imperial Fleet, or Tamin on the republic fleet, for 25,000 credits. There is no excuse to not having a security key - not when you're missing out on this pet!

Once out, the Mouse Droid looks like this:

Rhythm Augmentation Droid

Technically this isn't a vanity pet, but it's fun so it deserves to be included. (It will also take up one slot in your bag.) Say hello to the Rhythm Augmentation Droid - it serenades you for 30 seconds and you can get it from Toth, the Security Key Vendor on the Imperial Fleet or from Tamin on the Republic Fleet, for only 55,000 credits.

Once out it looks like this:

Hutt Observer

The Hutt Observer vanity pet can be bought from the Collector's Edition vendor, Nongta, in the VIP Lounge on the Imperial Fleet or from Jhaffus on the republic fleet for 25,000 credits.

Once out it looks like this:

If you don't have access to the VIP-lounge you can buy it from a bartender in the cantina for 1,000,000 credits.

Little Sandcrawler

The Little Sandcrawler vanity pet can be bought from the light side vendor, Lord Vassanar on the Imperial Fleet or Mira on the Republic Fleet, for 25,000 credits. They live in the Galactic Trade Market-section. You need to be at least level 3 light to use it.

Once out, the sandcrawler looks like this: