Probably another stupid guess, but Donkey Kong Country?

Outcast?

Riding an ostrich? One game comes to my mind immediately - Joust!

But if you are not old enough you have probably never heard about it ;)

Rock socks, Ghorpm!

I had Joust for my 7800. You may remember that when you were unseated (died), your mount survived and ran off the screen without a rider.

I'd enjoy a modern and pretty Joust with similar gameplay, I think.

Your turn!


edit:
I remember little of DK Country mounts, and I've only just looked at some Outcast screenshots, but they both seem to be reasonable guesses.

WOW! You've totally made my day right now! And I own you an apology because I assumed that nobody would post a riddle about Joust. But it comes from my bad experience - you've no idea how many times I've heard "What is this crappy game that you are playing?!" or something like this. Heretics! Is one of my favorite games of all times!

Give me some time, I'll draw something soon

EDIT: here it is. Sorry for a very primitive paint drawing but I'm half asleep already and I'm going to bed soon.

Castle Master?

No. There are other clues than just a castle there. I know - they are badly drawn but at least I hope they should be readable ;)

Castle of the Winds?

It was readable after all! Your turn!

Drawings just get harder and harder to guess!

For you and I it does. Everyone else seems to be doing just fine.

Me feel brain fall asleep soon. Must go bed, after just few more cat picture pages, yes.
Here picture.

Far Cry 2?

Correct! Your turn.

Beware. Incoming ugly picture....