Google is your best friend:
http://www.yt2gif.com/
i didn't check out that site thoroughly, but usually, those kinds of sites degrade the quality/put stuffty borders/watermark stuff.
if you really want to make a nice gif, get a demo of a program like photoshop and find a website or program to download the video file. then, import the video frames into layers, and delete all the layers you don't want. finally, save the file as a .gif and save for mobile devices.
something like that, i think. there are tons of tutorials on how to do it.