Just curious to know what they would be?

I can't really remember anyone riding anything but horses and silt striders.

I also don't think it's very lore friendly to be riding dragons, or giant eagles or anything like that.

Do khajit ride lions/tigers?

I need a list of things used as transport in TES

Well, there's the http://www.uesp.net/wiki/Lore:Khajiit#Senche-raht as well as Aldmeri Sunbirds, which are either living birds, or giant flying ships made of magic.

I always imagined the Altmer riding some type of avian mount into battle, but something more reminiscent to the Chocobo then some grand flying beast. The Orcs are actually said to ride giant wooly centipedes if I'm not mistaken, so that apparently is a thing.

The Dunmer have their Guar. I believe ZOS has expressed interest in introducing them as mounts at a later date.

The Khajiit are known to ride Senche and Senche-raht Khajiit into battle. ESO, weirdly, features "Senche-tigers", who 1) are much smaller than the Senche and Senche-raht are described to be, and 2) don't seem to be a khajiiti subspecies at all. And for some reason, some Senche-tigers aren't tigers, but rather lions or leopards. It's... weird.

The Orcs are said to keep herds of giant, wooly centipedes. I'm not sure they'd make good mounts, but hey, it's something.

The Altmer already have their Sunbird spaceships, so giant eagles (made of sunlight!) wouldn't be completely out-of-place. But ESO has generally avoided the weirder, more fantastical elements of Altmeri culture, so I doubt we'll see them.

If ZOS wanted to be really adventurous, they'd give us Imperial moth mounts.

http://tamriel-rebuilt.org/files/TR_Artbook.pdf

Borrowing inspiration from TR, I would be the Ra'ga would ride camels, or if we go something more fantastical I believe there is one in here with a lizard like creature used as a mount.