I am severely disappointed with everyone who posted previous to me in this thread. Though most of these are actually great AMVs, they can hardly compare to one of the most well done and magnificent AMVs of our time. That being of course:
This is a thread as though it was meant for me. Since your asking for very emotional ones I will post those. This one is my favorite emotional amv and probably my favorite amv in general (Bakemonogatari). I promise, it is awesome.
Lets see what else I got...
This one is quite dark and is a crossover between toradora and Index
Last but not least...this one doesn't really fit the emotional theme, but it explains the importance of talking to your partner about your desires and what you are looking for in a relationship (don't get turned off that this is from a musical...it's quite funny once it gets into it).