BA BAH-DOH

AF: LAX-PPT, BKK-SGN, BKK-HAN
KQ: BKK-CAN, BKK-HKG
MS: BKK-CAN
ET: BKK-CAN
QF: AKL-LAX

CO: Check out the CO Micronesia operations. Many flights in that region that don't start/end in GUM.

There really are tons of them out there.

I stumbled across a weird one the other day.
Someone was listing a PIA flight from IST-AMS
PK 761 ISB-IST-AMS

PIA also used to do JFK-CDG - onward to Karachi, if I'm not mistaken


Also-
Apparently Air India is canceling that EWR-PAR flight (and presumably the ongoing flight where ever it goes to/from there).

My mother was booked on it for March and she had to be accomodated on CO.

PPT is part of French Polynesia, so this is not an example of a 5th freedom route.

KL BKK-TPE

There are thousands of intra-EU ones. Just look at Irish-registered Ryanair's bases throughout the UK, and Belgian-registered VLM's base at LCY!

HY (Uzbekistan Airways) has, I believe, has the rather odd JFK-RIX. Turkmenistan Airlines used to to some bizarre stopover in BHX, but I don't think that's still going.

Jet Airways, SFO-PVG
Northwest Airlines, NRT-PEK
United Airlines, HKG-SIN
Thai Airways, HKG-TPE

Jet has quite a few:

YYZ-BRU
EWR-BRU
JFK-BRU

Dont forget MH:
EZE-CPT (and on to JNB-KUL)

Copa has all kinds of stuff such as TGU-SJO and many more...

JL operates YVR-MEX in addition to the previously mentioned JFK-GRU

EK has a slug of trans-tasman flights eg. SYDAKL etc

I think there are many carriers on the Oz-NZ route.

BA also have BKK-SYD and SIN-SYD.