I have one too and I absolutely love him! I'm not sure if all OTTBs are like him or just him, but when I bought him he had 3 months of pasture time under his belt and was ready for his new life. He is very affectionate, but at the beginning had issues with personal space and mounting up was a focus point of training as he liked to walk off once I got up. He did tend to crowd and he had NO herd manners. The lead mare would lay her ears back at him and he'd walk right up to her, completely oblivious to her cues. The first 4 months he came in daily with new bites and scratches. And once came in with two swollen joints from a bad kick that I feared would cause permanent lameness - thankfully didn't!
I spent my first few months with him doing just walk-trot-stop exercises in a confined area. And while he sometimes seems to have a few screws loose in his head - he took FOREVER to figure out how to walk through a narrow space without hitting either side, and has a horrible habit of walking into unmoving objects expecting them to move out of his way - he is an honest, hard working horse. He'll try anything. He loves to jump, and we play lots of pasture games the include him trotting after me around different objects and jumping fallen logs. He's the first horse to greet anyone in field. And despite the bad rep some OTTBs have about being a little on the pshyco side, he actually has a very sane mind. He never runs off with me, has never once tried to buck, or rid me of his back. He goes walk-trot-canter easily and on command, and - only when I ask - he'll give me his absolute fastest gear.... however this gear requires a loooong stretch to stop from. And he's pretty much bombproof.
I wouldn't reccomend a horse like him to a complete beginner because while he is a great horse, for the first few months I did have to be on my guard and willing to tell him 'no'. And unlike the lazy ranch horses who stop when the horse in front stops, you have to be willing to ask him for what you want, be it stop, go, back up, etc..
I can't tell you if all OTTBs are like him, as I've only known him well and have handled only two others.. one of which was a old school horse who hadn't seen a racetrack in 10 years, the other a trillium level jumper who I thought was beautiful but whose owner thought was a nut case - but I never saw this from the mare for myself.
This is my horse, Nikki:
^ He goes through anything. ^
When I first started working him, I wanted him as sane and calm as possible, thus we spent a lot of time bareback in a halter after I had established a level of trust with him.
^training him to stand while I mounted, I had my bf hold him while I got on from a lovely plastic bucket... I know... not the safest thing around to mount from, but I didn't want to land on the wooden mounting block if I fell XD But I never have fallen from Nikki
^I now trust him to do anything on!