I agree with some of the answers here, but I think there is another difference between "te amo" y "te quiero". "Te amo" could be translated like "I love you" but also could means "I'm in love with you". "Te quiero" just means "I love you" or "I like you". I think It never means "I'm in love with you" or "I have fallen in love with you"

te amo is more dramatic than te quiero, but you also can say to your girl/boyfriend te quiero

we dont say te amo that often, but it is used mostly for lovers. te quiero is more common but still you can say te amo to your parents or relatives. when you say te amo to your boyfriend is because you are really into him but even thogh you can say te quiero

Hello dear Emma, i believe the answer is based in the amount of loveliness you have for some one, amar y querer is not the same and i strongly recommend for you to listen to a song we have as answer to that question, very well developed i must say,the song is, "amar y querer" the singer is José josé, very popular singer in México, he will explain that very throghlly to you. I hope this will help you.

I wrote a little, but careful answer to that question myself a few days ago: http://www.italki.com/docs/B0B15E51-8E1C-4BD0-80CD-58D0C031BC44.htm