Well, probably not but they do allow you to do combos in this game that you are not able to execute on normal hit. I found this Akuma vs Abel video in the SRK SFIV Video Thread earlier today and seemed like a pretty good video to break down when it comes to counter hits in SFIV.
The way counter hits work in this game is certain attacks will give you more frame advantage if they land as counter hit which allows you to link into moves that you normally wouldn't not be able to link into. (According to the Master Guide, light attacks add 1 frame of hit advantage and medium and hard attacks add 3.) For instance, one night at the arcade here I was able to combo c.mp into c.mk with Sagat because the c.mp was counter hit and added 3 frames of hit advantage. You normally are +4 on normal hit with a c.mp and c.mk with Sagat has a 7 frame start up, so if you do the math, you do not have enough of a window to link the two moves together. But since in this situation with the c.mp being +7 ([4 frames of hit advantage for normal hit] + [3 frame advantage for the counter hit] = +7 total frames of hit advantage) because of counter hit, I was able to link into the c.mk with its 7 frame start up.
So if you watch in the video below, Akuma is able to perform a pretty lengthy combo because the initial MP attack is counter hit. The thing to understand about this video is the combo could have been a lot more damaging under the right circumstances. At the end, he goes for c.mk into fireball but he is too far away for it to connect. If he was closer and had more meter, he could have finished that combo with c.mk xx fireball xx FADC -> c.mk xx fireball FADC -> c.lp -> Hurricane Kick combo. The combo would have been somewhere around 15 hits and would have most likely stunned or killed his opponent. This just goes to show how little we have seen of Street Fighter IV and it's combo system.