I think of a bland yeasty beer like a German hefeweizen but without any clove or banana. Popular examples have included those from Widmer and Pyramid. Not a favorite style of mine at all, boring. The thing that first defined it long ago was the haze. These days, of course, haze is no big deal. Add some crap to it, sure, that might make it taste better... but then it isn't a true American Wheat anymore either, at least by my mind's definition, which tells me it's yeasty but otherwise bland.
Shock Top and Blue Moon are somewhere in between two styles, more like a Belgian witbier including coriander, but made with American ingredients. Not what I would consider an "American Wheat" though. There is too much flavor in a wit-like beer to be part of the old "American Wheat" style. Not that more flavor is a bad thing. Like I said, I don't really like the style.
Bell's Oberon, IF it is truly part of the American Wheat, is probably the best example of such a thing. The yeast here makes the beer interesting enough to want to taste it again and again. Oberon is good stuff.
I would be remiss if I did not mention New Glarus Spotted Cow. This beer fits the bill rather perfectly. And... it sucks, IMO. Our club met Dan Carey once, asking what he really felt about this beer, and he basically shrugged and said, "well, it pays the bills." I couldn't agree more!