While usually we associated towered airport with at least Class D airspace designation, there are some weird combos that can be found through out the US as well.
KNXP: Class D for an untowered airport

KNXP is one such example where the airport itself is shown as an uncontrolled airport but has a Class D airspace surrounding it. If you look into the Chart Supplement, you will find an explanation there: - MISC: CLASS D AIRSPACE EFF NOTAM ONLY, OT CLASS G.
KFNL: Towered but Class E

KFNL is an interesting example. It is not only one of the rarer Class E towered airport example, it also was one of the only few airports with a remote tower in the US. (It looks like the project was on pause after October 18, 2023 as the vendor decided to leave the pilot program and the airport now uses a mobile control tower instead.)
Can I go bust the class E?
While there is no requirement of ATC contact in the Class E airspace in general, §91.127 does require you to be in contact with the tower within 4nm and 2500ft AGL.
Pop-up Towers
Airports can also only have towers sometimes: Sacramento’s McClellan Airfield (KMCC) is a Class E airport that would have “pop-up towers” during busy seasons, like during fire fighting operations and air shows. That’s why it’s always important to check NOTAMs before you go somewhere!
KSXS: Towered but Class G

These are getting harder to find and the remaining examples are usually military heliports. Other examples I found online are usually airports that used to be in Class G but has since built a tower and was in the process of being converted to Class G and because airspace designation is a legislative process, it stays Class G until the the rulemaking process is completed and get upgraded to usually Class D.
Class G is uncontrolled, right? Right!?
While Class G is uncontrolled airspace, §91.126 does require you to be in contact with the tower within 4nm and 2500ft AGL. Since their outline are not charted, watch out for it!
KPSP: Class.. D and a half? (TRSA)

Flying into KPSP is kinda like flying into any other Class C airports, you talk to the Palm Springs approach, who then hand you off to the tower. Easy. Wait, hold on but this is not a Class C airport though? This is a TRSA (Terminal Radar Service Area), as the name implies, it provides TRACON (terminal radar approach control) services in the area. It sits in Class E airspaces so the services are optional. These areas usually are set-up around busy Class D airports and might be upgraded to Class C/B in the future (or get stuck in TRSA limbo forever …).