Server-side auto-minify?
You can try nginx's third party Strip module:
http://wiki.nginx.org/NginxHttpStripModule
Any module you use is just going to remove whitespace. You'll get a better result by using a minifier that understands whatever you're minifying. e.g. Google's Closure javascript compiler.
It's smart enough to know what a variable is and make it's name shorter. A whitespace remover can't do that.
I'd recommend minifying offline unless your site is very low traffic. But if you want to minify in your live environment I recommend using nginx's proxy cache. (Sorry but I don't have enough reputation to post more than one link)
Or you can look into memcached for an in-memory cache or Redis for the same thing but with disk backup.
I decided to do this through PHP (mostly because I didn't feel like writing a lighttpd module).
My script takes in a query string specifying the type of the files requested (js or css), and then the names of those files. For example, on my site the CSS is added like this:
<link rel="stylesheet" href="concat.php?type=css&style&blue" ... />
This minifies and concatenates style.css and blue.css
It also caches the files using XCache if it's available (since minifying is expensive). I actually plan to change the script so it doesn't minify if Xcache isn't available, but I have Xcache and I got bored.
Anyway, if anyone else wants it, it's here. If you use mine you'll need to change the isAllowed() function to list your files (it may be safe to make it just return true, but it was easy to just list the ones I want to allow).
I use Microsoft Ajax Minifier which comes with a C# library to minify js files. I use that on the server and serve up a maximum of two minified .js files per page (one "static" one that is the same across the whole site, and one "dynamic" one that is specific to just that page).
Yahoo's YUI compressor is also a simple Java .jar file that you could use as well.
The important thing, I think, is not to do it on a file-by-file basis. You really do need to combine the .js files to get the most benefit. For that reason, an "automatic" solution is not really going to work - because it will necessarily only work on a file-by-file basis.