oops! I meant to answer Arcane Trickster, not Arcane Archer. Not for me, but for my wife, whose flagship character has levels in AT. I've never seen anybody play an AA, though I think it looks like a fairly workable archetype, moreso than many others I've seen.
I played a Mystic Theurge briefly in an abortive attempt at Demon God's Fane.
My observations have lead me to believe that if you want to play a rogue, but your DM, through in-game motivations, drives you into several levels of arcane spellcaster, Arcane Trickster is a strong option. It allows you to give up very little of what the rogue class would have offerred, while simultaneously offerring much of what is offerred by the wizard class. This would never be a class to shoot for from the beginning, because multiclassing spellcasters just hurts too much, but if you're already up the creek, this isn't a bad boat.
Mystic Theurge, on the other hand, is a disaster. I built this character, at ECL 15, from the 3.5 DMG preview on the Wizards' website before 3.5 came out. Naturally, like many others, I thought that the MT would be ridiculously overpowered - part of the reason I wanted to play one was to see if I would ever be willing to allow one of my players to run one. Usually, I'm the DM, and game balance is entirely in my lap; nobody else could give a rip. Access to divine and arcane magic didn't begi to make up for missing the two highest spell levels in both. Her spell DCs were a joke, because I'd split ability scores between INT & WIS. She lacked most of the spells that would have actually made a difference, and combat was totally not an option for this PC. She would buff the other PCs before fights and heal them afterwards, and sometimes her divinations were helpful, but basically, the other three PCs did everything of significance and she was just a third wheel. I'm glad that I was playing two PCs, because my straight human monk 15 whooped tail on everything he encountered and was fun to play. Without him, it would have been a bore.