It's definitely doable, since I've done it and never had any particular problem. However, a lot of people don't like the idea since if one of the services gets broken into the attacker can easily mess with the other service. Quite a lot of people will probably tell you that you should only run one publicly available service (besides ssh) per machine, and that's probably good advice if you have the resources to get that set up. But you definitely can run Apache and BIND on the same machine.
Incidentally, if you are going to run multiple services on the same machine you probably should consider running each in a chroot jail so if something goes wrong with one service it's harder (though not completely impossible) for it to affect the other service.