There's no hard limit for the number of services running on a Windows Server 2003 machine. Instead, the number of services you can run is largely limited by the size of the heap. Once the heap gets exhausted, you may start to run into problems like services suddenly failing or services failing to start.
To see if your heap is being depleted by services, you can either check the event log or you can use Desktop Heap Monitor, which can be downloaded from the Microsoft Download Center at http://www.microsoft.com/downloads/details.aspx?FamilyID=5cfc9b74-97aa-4510-b4b9-b2dc98c8ed8b&DisplayLang=en.
Mitch Tulloch is lead author for the Windows Vista Resource Kit from Microsoft Press, which is THE book for IT pros who want to deploy, maintain and support Windows Vista in mid- and large-sized network environments. Mitch is also the author of Introducing Windows Server 2008, the first book from Microsoft Press about the exciting new server platform. For more information on these and other books written by Mitch, see www.mtit.com.