I personally don't like them much.
I've owned a few and one was very well trained at what I wanted to do, and we'd do quite well in competition, but he just had a pretty bad personality, and a bad way of dealing with things. I felt that no matter how much training he had he'd always revert back to his track way of being in times of stress. He'd always jog and lean and bolt eventually and I did so much work with him. I've had other ones too and they all had their issues, I've seen some good ones and you hear about them all the time, and then I've seen so many bad ones that people either complain about or don't talk about, or make excuses for.
I find a problem with Thoroughbreds is that they're bred to be fast. That's it. They're (mostly) not bred for their personality or intelligence or health. Which means many of them are lacking in these areas. They're (generally) not bred to be show-jumpers or dressage horses or anything like that. That is simply not their purpose. While some do excel at these sports most do not. Many Thoroughbreds are used in these sports and they do alright, but not as good as a purpose bred horse would do, and often get stressed and injured in the process. Why would you buy a TB bred to be fast for dressage when you can buy a horse that is bred for dressage, and bred to have a good personality and be sound? The reasoning there (for most) is that TBs are cheap, and its true, they are.
I guess a purpose bred Thoroughbred for like eventing or something would be okay, because it wasn't messed up from the track and it was bred for temperament, health and with a purpose that was suitable. I probably still wouldn't buy one but I'd have no problem with them. Most aren't though, most "unraced" TBs are those who simply never made it to the track.
On top of that TBs don't tend to live for as long, they're more prone to injury or lameness (in my opinion) and they require more upkeep (feed and rugging) and often more hoof care.
There are many TBs out there that are good, and that people love and have done well on and I am sure many people will share their stories here. But there are many that aren't good in any way.
Each to their own, I just worry that many people jump into owning TBs without understanding them but just get them because they are the affordable option.