Is there a list of aircraft which squawked 7700?
An ATC facility probably has a method of recording any aircraft they dealt with each day which declared an emergency, via the transponder code or otherwise.  One is probably safe in assuming that this information is passed along up the food chain for some sort of collection at a national level, although such an aggregated list may not be immediately available to the general public.  My first guess is that a FOIA request might be able to get what you're looking for, although if the requested scope is "every emergency aircraft at every facility in the US over the last two decades," you may be out of luck.  (That would be a huge volume of data anyway.)

Understand a couple of things about declaring an emergency:


Most aren't accompanied by actually squawking 7700.  Of the (relatively few) emergencies that I've declared in a couple decades of military + civilian flying, I can't think of any that required us to change the transponder code -- we declared the emergency with ATC on the radio, kept our assigned squawk, and did what we needed to do.
Many aren't related to the aircraft at all.  I had occasion about a year ago to ask our airline safety department what the most common cause was for declared emergencies in our operation, and was told that far &amp; away, sick passengers (medical emergencies) were #1 by a huge margin, and everything else (which includes all the aircraft-related events) was far down in the weeds in comparison. Given that, seeing that aircraft 123XY declared an emergency 5 times last year doesn't necessarily mean that it has had more mechanical issues than its fleetmate 234XY that only did so once; it may just mean that 123 got more than its share of sick passengers.


In fact, in airline operations at least, mechanical issues are almost always caught on the ground, so an aircraft with "gremlins" will usually manifest them in terms of maintenance delays and cancellations, rather than in-flight emergencies.