With you having a old version such as that here is what I would do. First of all take a backup of your database:
http://codex.ww.wp.xz.cn/Backing_Up_Your_Database
Then make a copy of all your files. I would then do a local install of the files and import the database (find and replace all URLs before doing this) using PHPMyAdmin.
Now you have a complete copy of your site locally. Upgrade it to 2.8 and see what happens. If all is well you can do it on the live site. If it fails you can investigate further without messing around with the live site.
Formatting (i.e. theme) shouldn’t break, though some things may not work so great.
For themes and plugins, I’d take the time to research them and see if they’ve been updated recently. If so, the odds are you’ll be okay, but check what other people say.
If it’s your own home-grown theme? Check this: http://ottodestruct.com/blog/2008/wordpress-27-comments-enhancements/
