You're free to use any font you want (such as Twentieth Century) in your design and distribute that design in a logo, book, etc. It doesn't matter whether it's commercial or not. The main caveat is that some foundries restrict the ability to embed fonts (such as in PDFs) (and some are picky about using it on the web), but that only applies to those situations. I am pretty sure that Twentieth Century will not have that restriciton, but if you want to be sure, you can search for the foundry and check out their EULA. Again, this is only if you need to create PDFs, Flash, etc.; normal logos (JPEG, GIF, outlined type in EPS, etc.) should be fine.

The main point of license agreements is to state on how many computers you can have the font and to prohibit copying, pirating, modifying, and the like. There are numerous permutations, but you're completely in the clear for what you're doing.

I think mrjono is saying he acquired the font in a suspicious manner.

Well, my quick edit put my post below yours, so sorry for mixing things up.

If you did acquire the font illegally, then I'm not sure as to the legality of making a logo with it -- I'd hedge on the side of that not being allowed. But Twentieth Century comes with Windows, I believe, and if you didn't get it legally, you can buy a version for about $20 from myfonts.com . Worth it for a clean conscience, I hope.

Hi,
thanks for the advice! the TW font was installed on my laptop when i got it, i haven't downloaded it from anywhere dodgy. the school i'm doing it for doesn't really have much of a web presence and as far as i know they don't intend to promote the departments anywhere outside of the school or on the web so i think what auricfuzz told me there should be fine. i'm starting a degree in graphics in september and really want to learn typography inside out so i guess this will be a good place to start!
thanks again to you both.

Just to summarize, since you got Twentieth Century with your computer (as I did), you do not need to be afraid of using the logo on the web or in outside or commercial publications -- otherwise many logos that we see everyday wouldn't exist!

You're very welcome, and you're right -- this is a fantastic place to learn about typography and type design!

also, check out typestudent.org

It is Dan Gayle's introductory resource center for those in school or learning about typography and type design.

Whoops. I wish I had known you were gonna do that! I just took the site down for an upgrade!

Oops! Sorry. :)