When you say multitasking, lots of people think doing one thing while you're doing something else. For some people, the image of someone on the phone while driving comes to mind. Throw in a burger and some call waiting and you're getting to the point that most sysadmins operate at every day.
I'm going out on my own here by saying that I don't look at multitasking as a bad thing intrinsically . Other people have different opinions, but I think that multitasking really does allow me to get more done, as needed.
Pushing my judgment in this direction is the fact that I know my requirements are not "Do this, do this, do this, do this, and do this, and have them all done by the end of the day". It's "I need this, this, this and this by lunch, and this, that this that and that done by the end of the day". If I were to stop multitasking, the number of things I get done every day would half, at least. Making things easier on me is that not all of my tasks need direct supervision. Some scripts I run need checking up on to see if they're done, but if they haven't finished yet, I don't need to mess with them. This makes it possible for me to sync testing and production, replay database transaction logs, have an IM conversation with someone in another office, and write documentation, all at the same time. Doing them individually is completely inefficient.
On the other hand, some things don't compliment each other. Writing scripts and replying to email, for instance. If you're writing anything other than a completely incidental script, being drawn out of it for email means you've got to re-find your train of thought. You lose lots of time. The same goes for any in-depth activity, like configuring a lot of networking equipment from the CLI, or running an detailed query.
In the end, though, it's really up to you to decide how much (and what kind) of multitasking you can take. And regardless of what anyone tells you, it can be learned. When I was in tech support, I quickly became able to IM, email, talk on the phone, and communicate with supervisors all at the same time, and I certainly wasn't the only one, by a long shot. It comes with practice.