In the US, are there any operational control towers located in surface-level Class E airspace or in Class G airspace?
There are a handful of towers still in Class E/G airspace. They're rare, but they do exist and are something to watch out for during preflight planning.
As of April 2021, here's the airports I know of:

KJYO - Leesburg, VA
KPCA - Picacho ARNG, AZ
KTNX - Tonopah Test Range, NV (inside restricted airspace)

I wouldn't be surprised if there's others I missed, these aren't really cataloged anywhere.
Many of these do eventually become proper Class D airports once they have proper weather reporting capability. For example, KTRK (Truckee, CA) was an infamous one on the west coast that just got its Class D ring in 2017.
You'll also see temporary towers pop up via NOTAM for special events. These NOTAMs don't change the airspace designation, since changes to airspace need to go through the formal rulemaking process.