My opinions on both SonAmy and ShadAmy:

ShadAmy-
A lot of people think Amy Rose is better off with the 'bad boy' type, instead of Sonic. She seemed to bring back Shadow's memory of Maria in the games, therefor I think they are very close friends. They have only hugged once, when Amy mistook Shadow for Sonic (even though they look NOTHING alike). But once she realized that he wasn't responding, she let go and found out that she was hugging Shadow, not Sonic.
In Sonic X, their relationship seems to be a little bit different, considering that Chris Thorndyke takes the place of Amy's job..... reminding Shadow of Maria (which I think is kinda awkward since Chris is a boy, Maria is a girl).
My final thoughts:
Amy and Shadow have a strong bond, and I think that he will keep his promise to her.


SonAmy-
My favorite Sonic couple! I mean...... not just because my favorite colors are pink and blue, but because of evidence:
In the games:
It starts off with Sonic rescuing Amy from Robotnik.... after that, she became his stalker (lol). I could tell that in the beginning, Sonic only liked Amy as a friend, like in Sonic heroes, Sonic CD and a couple more of the early games........
Then when it got to the stuff like Sonic riders, he seemed to be more.... 'protective' of her safety. This showed even more in Sonic riders: Zero gravity, when Sonic, Amy, Knuckles and Tails encountered Jet the hawk. First of all, he pushed her out of the way when the robots were trying to run them over. When Jet appeared before them, Sonic put his hand in front of Amy. Don't say that doesn't mean anything, cause it does mean that he's trying to make sure nothing hurts her. Then, when Jet accused Amy of stealing the Ark of the Cosmos, I could see that Sonic's face expression wasn't very happy. He stood up for her by saying "Hey! Hold up a minute. Girls hate guys who rush them, Jet." In Sonic chronicles: The dark brotherhood, you can choose what Sonic says. If you're nice, Amy will ask if he cares for her or not. I have this game, so I would obviously choose "Yes." And...... she might even ask to go out with Sonic, and the choices can include acceptation. Sonic and the black knight surprised me in the end, where you could hear Sonic and Amy talking, saying stuff like "And that's what happened.", "That's the LAMEST excuse ever! You just forgot about our date!", "I swear it's the truth! No.... wait, Amy! DON'T TAKE OUT THAT HAMMER!" and "You get back here! SOOOOOOOOOONIC!!!!!!!"
So the whole thing was just Sonic explaining why he missed his and Amy's date. That really made me crack up :D
Sonic Unleashed showed that Sonic was disappointed when Amy didn't recognize him in werehog form.... and he even saved her from some of Dark Gaia's monsters! But when she woke up, he quickly ran away, afraid of what she would think of him as a werehog...... probably a monster. But, Amy doesn't care about appearance!
In Sonic X, their relationship grows further as Sonic and Amy have.................. some kind of a flirtatious thing going on..... :)
My final thoughts: SonAmy is a wonderful couple and I hope with all of my heart that it will happen soon!