As others have mentioned, there's no problem having different wheels or tires. There are actually some very good reasons to have a larger tire in the back than in the front.
Larger tires allow you to run the tire at a lower pressure and gives you a cushier feel. Slimmer tires are lighter, reduce rolling resistance and aerodynamic drag, and give the bike a more nimble feel.
Since rear wheel supports more weight, it makes more sense to put a larger tire in the rear. A larger tire. This isn't as much of a concern with the front wheel since it's supporting less weight. Also, your arms absorb an unexpected bump a bit more easily than your butt does. That being the case, you can put a smaller tire up front to make the steering more nimble and reduce weight, rolling resistance, and drag.
For all the same reasons mentioned above, it's also relatively common to see rear wheels more stoutly built than their front counterparts. This is most apparent on high-end race bikes, which can have almost twice as many spokes on the rear wheel as they do on the front. The rear wheel spokes are also crossed to give them greater strength while the front are often laced radially without any spokes crossing the others.