Unconverted Neopets are pets that retained their old images after the art overhaul of April 2007. The newly converted pets took on uniform positions regardless of colour or species so that customisation could be implemented, while the old ones kept their personalities by having whatever pose was normal for their colour/species combination.
Not all pets had the choice to stay unconverted. A select few colours, like baby, royal, or darigan, were left untouched while others were automatically changed. Basic coloured pets, starry, gold, shadow, and many others (even a few species of the "unconverted" colours) were turned without owners' consent. If your pet was not changed automatically, you would see a button next to them on your QuickRef page that says "#Name must be converted to be fully customisable. Click here to learn more."
UC pets can no longer be hit by colour-changing random events like Boochi.
Unconverted neopets are in high demand these days. They can be traded for pretty much any pet that you could dream of on the Pound Chat. While some users frown upon the objectification of these rare pets, they are seen as status symbols (much like draiks or krawks) and rich/old players are their most common owners.
*Cannot be fully customised (only trinkets, backgrounds, music, and foreground items can be added)
*Cannot show emotion or illness
List of Unconverted Neopets
There are a lot, so be prepared when you hit "Expand"!
If you have a UC pet, it is suggested that you DO NOT convert them.
They are rare, valuable, and completely uncreatable. You can never choose to change your pet back afterwards. If you prefer the new art, it is suggested that you trade for a pet of the same colour/species on the Pound Chat, or simply create a new pet in Pet Central. It's pretty much a loss to the entire community when someone chooses to convert!
http://www.neopets.com/~grattin has a list of all UCs and their estimated Pound Chat trading values.