Update: The newer versions of skype now have the ability to change the font size. Go to menus Tools, Options..., IM & SMS, IM Appearance, Change Font
The only problem with the new version is that the setting (change the font size) is no where near the actual thing you are setting! (the text in the IM/chat window). At least the absolute newest version has "share my screen" so that I can explain to my Mom how to change the setting by showing her on my screen.
Note, this post was written in May 2007, and no longer applies to the newer versions of skype (version 4 and newer, I believe)
Designers must respect users' preferences in regards to colors and font sizes. Another post discusses that. The interface belongs to the user. Don't mess with it, don't assume defaults, don't hard code colors.
So why am I talking about Skype? Because when clean, simple, usable design meets real-world issues of font and color preferences, there can be problems.
(only on the PC version of Skype. Mac Skype users don't have font problems.)
Setting the font in Skype chat (PC):
Font size must be between 4 and 12 point
This should throw up a few red flags. "Must?" "4 point?" In actual usage on todays high resolution screens, this could read:
Font size must be between ridiculously tiny and barely readable.
Some designer probably made the case that the chat window doesn't look good above 12 point, and this crazy restriction made it into the application somehow. And 4 point? What? This is an actual screenshot showing what 4 point looks like. Laughable.
Because of Skype's good, simple design, lots of people use it. Regular people. People with regular eyesight. Older people. Even people with poor eyesight. It's painful to watch my mother-in-law squinting, pressing her face up to the monitor, messing with her glasses...
So I said, enough is enough! I put on my geek hat and figured out how to force a font size larger than 12 point in Skype chat. Grandmas rejoice! Eye-strain be gone!
- Find the file "config.xml"
It's in the Skype folder under your login name and Skype id.
Example: C:\Documents and Settings\Administrator\Application Data\Skype\kmaageatopera\config.xml
Substitute your own windows user (if not Adiministrator), and obviously your own skype id (if not kmaageatopera)
- Quit Skype (if you don't remember your Skype password, see the warning)
Completely quit skype, don't just close the skype window. You will have to right-click on the skype icon in the taskbar and choose "Quit"
Warning You will need your skype password when you start Skype again. [1]
- Open the config.xml file using notepad
- Find this line about 1/3 of the way into the file:
<FontSize>12</FontSize>
- Increase the number to your liking
(I think 18 is comfortable. You could try 16, 20, etc. Bigger number, bigger font)
- Restart Skype
Since this is a "backdoor" solution, if you try to set the font again using the interface, Skype will complain with the above message. If you somehow "lose" your big font, just do the steps again to get your big font back.

--
[1] Regarding the warning about quitting Skype: Don't laugh. I've encountered people who never quit Skype because they don't remember their password. If you don't know your password, you will need access to
the email you used when you created your Skype account and go through the Forgot your password steps on the Skype login screen. If you don't your password or your email, don't do this font size thing, because you'll never get back in to your Skype account. Oh, and
be careful to
never exit Skype either. Seriously.