Different breeds that I have had as companions is quite a short list...
My first pony ever in germany... stubborn little thing. Not sure what breed he was tho.
Hannoverian, my first grand prix dressage horse.
Now off to america, I had my best friend an Appaloosa along with a few Quarter Horses.
As for horses I've ridden... Various, various breeds. I used to train horses in the last 5 barns I was at, and there was a serious variety of breeds present. XD
In addition to ponies, QH, TB, I've been on various gaited horses, friesian, lippizzan, andalusian, arabian, curlies, variety of draft horses and warmbloods... o.o