I am looking to install a Webmail client. However, my mail server is seperate from my Web server, though the two are on the same LAN (A router does port forwarding to my public IP). I've looked at some clients like Neomail, but they seem to need access to the mail server's mail spool. Are there any clients that will use, for example, IMAP? Even one that acted as a POP3 client would be fine.

Well yah, most setups actually involve setting up and running the webserver on one machine and mail on another.. and if you want to run a webmail client, just so happens you'll need to have apache running on it as well. If you can get two IP's, just setup the mailserver as mail.your-domain.com and the main webserver can still be www.your-domain.com and such..
Then setup DNS accordingly with your proper MX records pointing to the mail.your-domain.com and proper IP's, etc. No need to have the mail server fetch the mail from other server, etc... if that's the case, just setup the mail server on existing server and only have one machine serving webpages and email..

I've already got everything set up, DNS, Apache on the second machine, etc. I just need the name of a good Webmail script that will act like an IMAP or POP client. Can SquirrelMail do this?

Never mind, I got Squirrelmail working, and it's just what I need.

What made you choose Squirrelmail? I currently have webmail and I am not happy with it. I am trying to look at other clients but I am having trouble gaining access to tutorials to see if the they are user friendly. Do you have any suggestions for me as you have gone through the process?

SquirrelMail just seemed like the right tool for the job. I don't do much programming in PHP, but I had installed it on my second Web server, figuring it might come in handy. When I was looking for a WebMail client, I initially overlooked SquirrelMail because I'm not too familiar with PHP. I decided to give it a try anyway. I just downloaded it as an RPM and installed it on my box, and now it seems to go nicely. The Web server running it is running RedHat 8.0. It has an old Pentium 166 MHz, and 48 MB RAM, but SquirrelMail runs fairly nicely on it. To make it work you really only need an SMTP server and an IMAP server, and they don't have to be running on the same machine as SquirrelMail. You could even use it with your ISP's mail servers. Check it out at http://www.squirrelmail.org/.

also squirrelmail has a lot of plugin for you to toy with. I have went though a lot of webmail and pretty much they all look almost the same. Not extremely pretty and stuff, but it gets the job done.

I tried messing with NeoMail a bit, but I couldn't really get it to work right.

Have you tried IMP mail? It has a lot more features than squirrelmail, and it's a lot nicer looking. www.horde.org