Aside from SeDebugPrivilege, the other major privilege that is abused during escalation attempts is SeImpersonatePrivilege (leveraged in tools like Incognito). This privilege can allow the user to steal impersonation and/or delegation tokens that are present on the machine.
That being said, there are a number of administrative privileges that theoretically have the potential to assist during privilege escalation attempts, including:
- SeTakeOwnershipPrivilege (owning and modifying objects to elevate privileges)
- SeRestorePrivilege (write access to any file)
An exhaustive list would be difficult to compose, and I couldn't say with any degree of certainty that any administrative privilege could not be somehow leveraged in this way.
Furthermore, similar to how SeTakeOwnershipPrivilege and SeRestorePrivilege might be abused, a common method of escalation from Domain User that I see regularly involves overwriting binaries or other code that will be executed by a higher-privileged account. As such, write access to service binaries, System32, the All Users 'Startup' directory, application executables etc can lead to other accounts (Local System, Administrators) executing an attacker's code. I have personally found that poorly configured file permissions are a more common attack vector when escalating from basic users.
A good overview of different methods, including some of those above: https://www.netspi.com/blog/entryid/112/windows-privilege-escalation-part-1-local-administrator-privileges