I think he's annoying now, looking back at the series. He's supposed to be this know-it-all genius kid, which is annoying to pretty much everyone except his mom.
Wesley was annoying but it wasn't Wheaton's fault. It was purely Roddenberry's. The "kid genius" bit in sci-fi was tired way before TNG. The Wesley Crusher character, if he had been toned down and pulled back, would have made a brilliant and successful proxy for the audience. Instead they made him a "weapon of contrived solutions." So sad.