I have had numerous requests to do some feature-by-feature explanation of what makes for good equine conformation. While there are some variations in ideal features from breed to breed, there are some general guidelines that can be used to evaluate a horse of any breed.
I'm going to start with the shoulder angle. This is a big one, because it impacts performance and how long the horse is likely to stay sound. A horse with a straight shoulder will have a more jarring gait. It feels jarring because it is jarring - the horse is also jarring his front legs with every step, which leads to more soundness issues as the horse ages - everything from arthritis to navicular is more common in horses with a shoulder that is too upright. The ideal shoulder lays at a 45 degree angle. The horse at the left has a shoulder that is too upright, or straight. The horse at the right has an ideal shoulder. See the difference?
Another thing I'm asked about a lot is what it means to be "downhill." A downhill horse has a croup that is higher than his shoulders. Again, this is a defect that has a lot of influence on performance. The downhill horse has problems collecting himself and using his hind end. It's hard for him to be light in front since his conformation throws his weight onto his front end. He may do ok for a discipline like western pleasure (though he will never be a top horse), but things like jumping or reining would be extremely difficult for him. His conformation puts more strain on his front legs and can contribute to stress related injuries and "wear and tear" problems like arthritis. Furthermore, a horse who is downhill is hard to ride - you feel the sensation of being thrown forward and must constantly compensate.
The horse at the left is downhill. You can see that although she is standing on flat ground and her hooves are in the same place, her croup is still much higher than her withers. Conversely, the stallion at the right is a bit uphill. Some disciplines actually prefer uphill conformation since it makes it easy for the horse to be light on his front end, facilitating maneuvers like flying lead changes or the high knee action desired in a park horse, but for others the ideal is completely level - an uphill horse is unlikely to find the level head carriage of the western pleasure horse easy to achieve. Don't be fooled by how low the stallion's back is. He's an aged stud, hence the back - the thing to look at is the line between the croup and the shoulder.
Finally, everybody who's new here asks about "nest." No, you won't find that on a conformation site. I made it up to describe horses whose necks run pretty much straight down to their front legs, either because they are so narrow that almost no chest exists, or because like the horse at left below, they have a fat and unattractive neck that blends right into the chest. (Like the term "cankles" where a girl's calves are so fat that they seem to run right down to her foot with no ankle inbetween). A horse who's got a "nest" isn't going to work out for a lot of disciplines. Can you imagine the horse at the left traveling in a huntseat or dressage style frame? Not going to happen. He can't. You often see "nest" in tandem with downhill conformation, as it is in the palomino stallion at the left. It will always be a struggle for a horse who is built like this to collect himself and perform. In comparison, the horse on the right below has a lovely neck. It is in balance with the rest of his body and he has a clean throatlatch (the area right behind his jowl) which gives him flexibility.
This comparison also answers another question I was asked to cover recently - how do you know a really top quality horse? What separates mediocre from excellence - not just conformation but overall look and appeal? The two horses below are both palomino AQHA stallions. You can sit and stare at them element by element, but the overall look should make an immediate first impression on you. Now, sometimes you have to look past that first impression and start critiquing the individual parts - some horses do have that overall look of excellence but still have a glaring flaw. But overall, the horse on the right really does scream "stallion quality" and the horse on the left screams "call the vet and get it gelded."