You could say, "Aw, you're too kind :) " or "That's very kind of you" but I would still add the "thank you" as well. For example, "Aw, thanks, you're too kind! :) " or "Thanks, that's very kind of you!"

You could say: "That's a very nice thing to say" or "I appreciate you telling me that" or "I'm glad you think so, that means a lot to me" or you could talk about the item being complimented. For example: the compliment: "You have beautiful hair". The response: "You think so? Hahaha, It takes me two hours to make it like this!" The compliment: "Those are lovely shoes you're wearing". The response: "I'm glad you noticed, I love them too, I searched all day to find them". BUT saying thank you is so automatic, it's a part of the culture like de nada. It's the polite and expected thing to say. You can say thank you and then add something like in the examples above.

One thing you could do which is extremely common is to say something which very slightly downplays the compliment without contradicting it - basically to show some humility. For example - Your hair looks really nice! - (As if pleasantly surprised) Oh, do you think so? Thank you! Or - I love your car! - Thank you. Yes, it's the most basic model, but it does look nice doesn't it? The idea is to effectively say "thank you for complimenting me, I won't let it go to my head."