Many theme frameworks and complex themes break up functions into different files and include them in one file called functions.php, sometimes within a folder called inc. If it’s your own theme, you can pretty much do what you want.
If it’s a theme to be released, end users typically look for a functions.php file as the default WP framework functions file.
The two latest default WP themes – twentyten http://wordpress.org/extend/themes/twentyten and twentyeleven http://wordpress.org/extend/themes/twentyeleven – use one functions.php file, as that’s part of the standard WP theme file structure.
But again, many themes use multiple files for functions, and if a user wants to work with or modify the theme, they will need a certain level of proficiency anyway. Code comments are helpful.