Using a matched set of tires front and rear is the norm. However, with time and experience I have learned how to use different tires to get the handling characteristics I'm looking for. To begin with, all the tires I'm talking about are sport radials. So they are in the same class of tire no matter what brand.
Each tire has different characteristics. For instance the Pirelli dragon I run on front is a soft compound race spec. It offers great grip, quick steering and outstanding stability at high speed.
A Dunlop 207 on the other hand offers the grip, but steers slower and can be twitchy at speed.
The Metzler Rennsport rear has good grip, but is too sensitive to painted lines and tar snakes.
Dunlop 208gp would be a great on all surfaces.
Even using the same brand, you can go with different compounds, like soft front and medium rear and different profiles. Some fronts are triangulated for quicker steering or rounded for stability. Going with different sizes, like a 180 rear instead of 190 effects handling. Keep in mind my only consideration is traction. I don't commute and rarely ride in the rain. Mainly Bonzai runs on central CA. back roads.
If you know the characteristics of a tire you can use it to your advantage. Like a sport tire up front and a sport touring rear for better mileage. I know, I know, this is not the way we were taught. But with tire technology as it is today, virtually all new tires are so close in performance, it wouldn't cause an unsafe condition. The only down side is the limited choices for the GS rims. At least it has 17 in rims and not 16 or 18s.

GSJack says:

I'm currently (between snow days) running a bias belted front Dunlop with a radial rear Metzeler. One think we need to consider in this overly litigious society of ours, the bike and tire manufactures have to be extremely conservative in what they feel they can recommend. They gotta warn you about everything. Won't agree to anything they haven't personally tested.

It's a personal decision though. If you don't feel you have enough experience, then be a little more careful in you choices till you've worn out a few more tires.

Think it's best to follow a couple of mix rules though. If you mix a radial with a bias or a bias belted tire, the radial tire should always be on the back. Also when mixing a bias belted tire with a bias tire the bias belted should be on the back. Both these rules are enforced in inspections across the big pond to the east, I'm told by the Avon site.

The ME33 front mentioned above was one of the best bias tires ever made, would mix with any other premium rear tire.