If they mean "don't make a fuss"
Give a really good version of something they already buy for themselves, like their favorite coffee or snack. It's simple, but it shows you know them.
If they mean "I don't need more stuff"
Give something that gets used up, like food or a treat. Nothing left over to store or give away later.
If they mean "I can't think of anything"
Ask a different question. Instead of "What do you want?", try "What have you been into lately?" People who can't answer the first one often answer the second one right away.
Write it down before you forget
Whatever they mention next, like a hobby, a place or something that broke, is your real answer. Kept lets you save a quick note the moment you hear it, so it's still there when their birthday comes.