Any wheel on any fork / frame? I have been braking for a bit too long with worn off brake pads on not so new rims so I basically killed them.

I currently have the stock wheels of an FX Trek 7.2 bike.

I will most probably change them. The thing is, that I would like to use the opportunity to install thinner tires. The current rims would support a range of 28-37mm wide tires.

The wheels I am looking at support 19-28mm wide tire range.

Will any of those new wheels fit on my bike without any further replacing? for instance because of the width of the fork?

How about brakes? I will obviously need to tweak them, but will it require more than just a set-up?
When buying new wheels, make sure the spacing matches up. Road wheels typicall use 130mm rear and 100mm front spacing where as most mountain bikes use 135mm rear and 100mm front. Hybrids vary, but it looks like this one has Shimano RM30 hubs which are 135mm spacing like a mountain bike.  However, if you find a 130mm spaced wheel you like, you can add spacers to make it fit the 135mm spacing of your bike if need be. 

I think it's worth a shot trying out a 700x28c tire on this bike without changing the wheels, which would be much cheaper than switching the wheelset.

FYI, I got my spec information for the wheels from here: http://www.firefoxbikes.com/hybrid_Trek_73FX.html