Some cavalry tips:
Always assume the spearmen are watching you
If you see someone walking in a straight line, chances are they're '~ing' you and will end up rearing your horse. You never want to risk rearing your horse, like Dex said you should be an opportunist, there will be a better chance later in the round (not to mention people will have low health later in the round!) to risk your horse for.
Horse Archers will kill your unarmored horse
If you're riding a courser or other lightly armored horse, you can get taken down with 3 arrows easily. I never recommend attacking a horse archer by yourself. If you're being pursued ride back to your team if possible or to the closest ranged ally, 9/10 times they will leave you alone. If your horse is armored then you can take more risks in taking them out.
Bumps r OP
In my opinion, bumping the enemy is the best way cavalry can help their team, setting their teammates up to kill them on the ground. Also when dealing with ranged, if you miss them with your lance/sword you can generally still run them over to prevent them from shooting for a few more seconds, and many lightly armored foes can even die in about 3-4 bumps later in the round. Your teammates won't be happy if you bump them either however.
And finally, always take the shot.