Microsoft gives a marketing list of reasons here - http://www.microsoft.com/windowsserver2008/en/us/why-upgrade.aspx
The unlisted reason I really like, because most shops seem to overlook it, is that Disk Partition Alignment is finally fixed by default - http://msdn.microsoft.com/en-us/library/dd758814(v=sql.100).aspx
You won't get this benefit if you simply re-attach your unaligned W2K3 disks, you need to go with freshly formatted disks. It also won't help if you have already manually aligned your W2K3 disk partitions.
answered Aug 01 '11 at 08:49 AM
For me I have seen much better usage of memory with Windows Server 2008 over Server 2003. Depending on your hardware specs you might be able to get around having to have Ent Ed of Windows. The disk partition alignment @KenJ mentioned is huge for SQL Server. I was very excited to hear that was taken care of in Server 2008. Running on an Operating System that is current is a plus by itself.
answered Aug 01 '11 at 09:48 AM
Could I suggest that if you take the step, go for 2008 R2. There aren't many differences, but stuff like Powershell have been improved upon and the clustering too, if that were to come up in the future.
The network improvements that @meltondba talks about really do work!
answered Aug 01 '11 at 11:59 AM