While I do love Exchange 2003, it is a solid product which has served us well for a long time, I think it's time to move on. Exchange has gone through 2 major revisions since Exchange 2003, and if you're not careful you'll end up with a product which Microsoft don't support any more (yes, it is a few years away, but it comes round VERY quickly!).
Putting software aside for a moment, your server is getting old and sooner or later the hardware will start misbehaving. Consider if you'll still be able to get parts for your server - disks especially. It's always the disks that fail! Consider also the cost of said spare parts - as hardware gets older and less of it is available, it does become more expensive.
This server is 4 years old, so assuming a 4 year server refresh policy, you'd be having this same conversation in 2014. By that time Microsoft will have probably forgotten all about Exchange 2003 and you might find yourself in the unpleasant situation where Microsoft have called end of life on Exchange 2003 and won't support you if you have a problem (which also means no security patches if any vulnerabilities are found). In that case, you'll be limited to third party consultants or community support from those who remember Exchange 2003 and how it worked.
Back to the software. Exchange 2003 is 7 years old now, which in terms of a Microsoft product is pretty old. Exchange 2007 and 2010 both make it pretty easy to migrate from Exchange 2003, but I'm not sure how long Microsoft will continue to make it so easy. There will come a point where it's just not worth Microsoft creating or supporting upgrade paths from older versions of Exchange because they are becoming increasingly rare. You can't migrate Exchange 2000 directly to Exchange 2010, and following that logic (which doesn't mean this is gospel) the next version of Exchange won't support migration from Exchange 2003.
Exchange 2010 does come with a lot of nice new features, which you may or may not use, but they are available nonetheless. One of my favourites is Resource Mailboxes with the calendar attendant, which allows you to create mailboxes for Rooms so you can invite them to meetings and use Exchange as a room scheduler as well. For a better list of new and shiny features, you'd be best looking around the Microsoft Exchange What's new page.
If you do decide to move to Exchange 2010, there are quite a few things you need to consider other than "just upgrading". You'll have to factor in the cost of a new 64-bit server (Exchange 2010 is 64-bit only), Exchange CALs, the cost of a Windows Server 2008 R2 license, Windows Server 2008 CALs, Exchange 2010 training and potentially some consultancy time to migrate you over.
Actually performing the migration from Exchange 2003 to Exchange 2010 is relatively painless and when it's done right, your users won't even notice. If you do have any other questions or problems, feel free to post another question here - we're a pretty friendly bunch (and we know a thing or two!).
I will be very brief on the Sharepoint requirement, as it's already been covered - definitely not required.