Hub Width
On road, mountain, and hybrid, the front hubs are 100mm in width. On road bicycles the rear is typically 130mm, where on a MTB it is typically 135mm. Measure this from your old hub, and DON'T stretch/force a different hub width.
Wheel (Rim) Diameter
The most typical road rim is a 700c which will mean the bead seat diameter of the rim is 622mm, and the typical mountain bicycle will either have 26" (559mm BSD), 29" (622mm), or one of each. There are many non-typical sizes, however, so see Sheldon Brown's Tire Sizing Page.
While some of this is rim sizing, it's the overall wheel size that matters - note that 29" MTB and 700c rims have the same BSD, but are unlikely to work well or fit at all (without serious brake modifications, to say the least).
If you want to see what various rim/tire combinations look like visually to compare them to your current setup, you can pick various ones (and see the resulting measurements in mm) on a site I built.
Brake Compatibility
You're either going to have rim brakes, which require rims specifically made with a braking surface and additional strengthening in that area (read: a bit heavier), or disc brakes which require a hub that can accept a disc rotor (and matching disc mounts on the frame and/or fork).
For best results, if you have rim brakes and don't plan to upgrade, get a non-disc hub and rim brake designed rim, and if you have disc brakes then get disc compatible hubs and rims without a braking surface (disc brake rims). This will lessen the additional (unused) weight and likely shave off some cost as well, but it is possible to have a rim brake rim with a disc hub.
With some road-style (caliper) brakes, you may have to adjust or even replace the brakes if you vary too far from their rim/tire clearance capabilities, so for best results stay somewhat close to what you had (or have the possibility of replacing brakes as well). V-Brakes, cantilever, and disc brakes are more forgiving on rim/tire size variances.
Tire Width
This is the most tricky part on a hybrid, as their tires (and thus rims) are typically somewhere between a MTB (1.8", 1.9", 2.0", 2.1", 2.3" being common) and a road bike (18mm, 20mm, 23mm, 25mm and 28mm being common). You'll need to use a caliper where the tire fits through the forks and frame to get a handle on your maximum size (allowing for some clearance) and then selecting a desired tire width up to that maximum.
Rim Width
This needs to match the desired / compatible tire width, see below (from Sheldon Brown's site).
If all of the above match, the wheel is good to go (with perhaps some minor brake adjustments).
