The Finder's View » Show View Options window only allows for fonts up to 16 points, when in theory you can use any font size you want. For me, changing the size to 18 points makes it that much easier on my eyes, and leads to fewer times when I'll have to use Universal Access. To change the font size, navigate to your user's /Library/Preferences folder. (note, the com.apple.Finder.plist file is in my home folder library, so [username]/Library/Preferences/, I believe this is due to more than one user on a system, so if you do not see the com.apple.Finder.plist file in Macintosh HD/Library/Preferences, check your home folder preferences).
In that folder, find com.apple.Finder.plist. Before you do anything else, make a copy of this file. Now open the original for editing. You can do this in a standard text editor, or but I strongly recommend you use a Property List (plist) editor to do so. Apple provides Property List Editor free of charge with the Developer Tools (it's in /Developer » Applications » Utilities; it's also included if you have the iPhone SDK - and it's also on your OS X install DVD, mount your DVD, and chose "Optional Installs", then "Xcode"). If you don't have the Developter Tools, and you don't feel like downloading gigs of developer tools for one app, you can use PrefSetter, a free alternative.
Once you've fired up your plist editor (or text editor), find the entry named StandardViewOptions. If you're using a plist editor, there will be a little disclosure triangle next to the name; click it to reveal that entry. You should now see entries for ColumnViewOptions, IconViewOptions, and ListViewOptions. Each should have a little triangle indicating it has sub-values. In each one, there will be an option for FontSize, which has a number for a value. This is the font size (in regular font 'points') for each view. Change the number to whatever you want. You will have to change the font size for each one to have it reflected in every view.
Save your changes (see note below), then restart the Finder using Activity Monitor, Terminal, or whatever method you usually use.
Other things to note:
I'm not sure what changes the text for the top part of the CoverFlow view. The bottom half is affected by the List View option.
If you hit Save and are prompted by a message that says "This file has been edited by another application," then hit Save unless you have changed your Finder preferences or viewing options since opening the preferences file and don't want to lose those changes. If you hit Save, you can always reapply those changes later. For instance, I changed the order of the sidebar folders, hit Save, and I had to swap them back -- no big deal, though.
robg adds: Depending on what you have or haven't changed in the Finder's view options, you may not see entries for each of these sections. If that's the case, you'll just need to change something in the view options for that view style first, then re-edit the file. Note that you can hang your Finder if you make a mistake here, so the backup file is important -- and I'd recommend opening Terminal before editing, too. That way, if Finder does get stuck, you can switch to Terminal, and use the mv command to rename/move your backup into your Preferences folder, then restart the Finder. (Or if you're using 10.5 and Time Machine, you can just find a backed up version from there and hit Restore.) Years back, we ran this similar hint about setting smaller font sizes for the Desktop view, in case you've got really good eyes.]