I've worked at places that do it both ways, and generally prefer having a separate account. It's actually a lot easier that way, contrary to what joeqwerty's reluctant users/customers seem to think:
Pros of using your normal, every day account for domain admin activities: Yay, all the administrative tools work on my workstation without runas! W00t!
Cons of using your normal, every day account for domain admin activities: Fear. ;) Desktop tech asks you to look at a machine because he can't figure out what's wrong with it, you log in, it has a virus. Unplug network cable, change password (somewhere else). When managers ask you why you don't get your work email on your personal blackberry through your cell phone provider you get to explain that they store your DOMAIN ADMIN password on their servers when you do that. Etc., etc. Your highly privileged password is used for things like... webmail, vpn, log in on this webpage. (Ew.) (To be fair, my account was blocked from the "change your password" webpage, so at least there was that. If I wanted to change my old LDAP password, which the webpage synced, I'd have to go to a coworker's desk.)
Pros of using a different account for domain admin activities: Intent. That account is intended for the administrative tools, etc., and not for email, webmail, vpn, webpage logins, etc. So, less fear that my normal "user" activities are exposing the entire domain to risk.
Cons of using a different account for domain admin activities: I have to use runas for administrative tools. That's just not that painful.
The TL;DR version: Having a separate account is just plain easier. It's also best practice, as it's least necessary privilege.