To quote from Rev. Lovejoy:
Shoo, short answer: "Yes" with an "If", long answer "No" - with a "But.
There are two types of driver signing, which complicates the answer. As usual any answers I provide are probably vague and can be overridden by standard documentation. In this case the documentation seems to be available on MSDN.
Driver Package Signing:
First there's the standard signing of the 'driver package' (all the files needed to install the driver) which has been around since Win2k. Signing your driver package allows you to avoid the "unsigned driver" popup, and allows end-users to determine whether your package has been tampered with. Personally I think it's goodness, but having never had to go through the signing process I realize it's easy for me to feel that way.
To sign your driver package your INF should have a CatalogFile directive in the [Version] section. The catalog file contains hashes for all the files in your driver package and is then signed to ensure it can't be tampered with.
Code Integrity Signing:
In Vista there's a new code-signing requirement. Kernel-mode binaries that load in 64-bit Windows Vista (or drivers on 32-bit & 64-bit windows that stream protected content) need to be code signed so that the OS can determine whether they have been tampered with.
From a quick scan of the documentation it sounds like this mostly affects the type of certificate you can use when you do your signing. The Code Integrity system (which checks your driver signatures when the driver is loaded) requires something called a "Software Publisher Certificate (SPC)", while regular driver signing can use either an SPC or a "commercial release certificate". However I believe that if you are installing a kernel-mode boot driver you have to make sure your binaries are self signed (signature embedded in the binary) while if you are installing non-boot kernel-mode drivers that you can use a catalog signature (signature embedded in the .cat file installed with the package) instead.
Regardless your driver package will still require a signature in order to get through installation.
So what does all this mean for UMDF?
UMDF drivers do not require Code Integrity Signing since they aren't kernel-mode code. However your driver package still needs to be signed so that it can't be tampered with & can be traced back to the author (or you continue to have unsigned driver popups). And if your package includes any non-Microsoft kernel-mode drivers in addition to the user-mode driver then the Code Integrity Signing rules apply to that too.
To finish with the quote from Rev. Lovejoy:
Uh, if you need additional solace, by the way, I've got a copy of something or other by Art Linkletter in my office.