My legs hurt. or My legs ache.
You could say either one. "Hurt" is a very broad term. If you get stabbed, it hurts. If you burn your hand, it hurts. If you eat too much, your stomach hurts. "I hurt" means "I feel some sort of pain."
"Ache" is a type of hurt. For example, if you eat too much food, your stomach will probably ache. If you have influenza, your head will probably ache. But if you get stabbed, you won't ache. Stabbing is too painful to be called "ache."
English has many words for different types of pain. This site has many good words, for example: www.aleve.com/understanding_how.html