Look at the top of the tooltip.

Unique means you can't have more than 1.

Untradable means you can't trade it to other players.

Unsellable means you can't sell it to an NPC.

Market Prohibited means you can't sell it on the market board to players.

Mounts usually have all of these things or none of them. The ones that can be given to others will show on the market board under the mounts category.