How can I change the system font size in OS X?

There's no built in systemwide means of adjusting the font scaling, short of running at a lower than native Resolution. In general, OS X is a fairly poor choice for everyday use at a distance of 10 feet from the screen. That said, you have a few options:

You can increase font sizes on an app by app basis. The main one you'll be concerned with, it seems, is Safari, where you can adjust the default display fonts for web pages under Preferences->Appearance, and on any given page, you can adjust the displayed fonts on any given page you are viewing with ⌘+.

You can also make use of the built in 'Zoom' feature in OS X. To enable this, under System Preferences, go to Universal Access and turn on 'Zoom'. This will enable you to zoom in on a portion of your screen at greatly increased magnification with a keyboard shortcut. Some people love this, but I find it slightly disorienting.

You might also want to investigate whether one of the systemwide 'theming' apps will work for you. The only one I know to work currently with 10.6 is ThemePark. You can probably find more info to assist you in taking this approach over at the MacThemes Forums, but be advised that this sort of 'UI skinning' tends to be frowned on by Apple and break frequently. It's something of a high maintenance option.

Finally, if you're really just concerned with home-theatre type usage here, you might want to look into any of the many FrontRow replacement apps out there that offer better support for Hulu, Vimeo, Pandora et al. Some of the major names in this field are Plex, Boxee and XBMC.

Apple doesn't provide the capability, but third party apps might. You could try TinkerTool which has a Fonts tab that lets you modify system fonts. I haven't personally used it for fonts (although I do use it to change other things like Finder prefs) so I can't say whether it works or not.

In 10.7 and later you can enable HiDPI modes by running sudo defaults write /Library/Preferences/com.apple.windowserver.plist DisplayResolutionEnabled -bool true and restarting.

The maximum effective resolution is half of the native resolution though, e.g. 960 x 540 for the internal display of my iMac:

Also this doesn't work with some (external?) displays anymore as of 10.9.