Given your predicament, I would grab *EVERYTHING* except the outer shell. (And if space is a total concern, I'd strip the tube from monitors and leave that but take the rest of the monitor parts--you can always find 80's tv tubes to put back in later)
That includes everything others have stated. I will list myself too just in case somethings missed.
1) Entire control panels. Yes, even the wood/plexi/carriage bolts/metal. STRIP them later,
2) All the wiring
3) All the transformer boards
4) All the logic boards
5) All the flourescent or incandescent lighting holders/bulbs
6) All the trim (except Tmolding) this means marquee holders, glass bezel holders
7) All the coin doors and mechs and attached wiring and buckets

All the locks
9) All the monitor bezel glass, plexi, and the formed surrounds (black plastic or cardboard)
10) All the wire clips and screws
11) Any cards/instructions/coins thrown/fallen inside (dip switch settings, service, money

)
12) Fans, Speakers, Speaker/air intake bezels and screws.
The only thing left at this point should be the cabinet+Tmolding and the monitor shelf/wood/metal montitor holder and the monitor itself.
DEPENDING on how much room you have, I would suggest that you would take all the monitors entirely (remove wood supports, but keep all metal ones and of course the metal frames). However if you are that cramped for space you cant take all the monitors, then learn how to safely discharge monitors and take everything EXCEPT the tube. (Remove the yokes and convergence rings).
If any are vector monitors (asteroids, tempest,etc..) by all means take everything including the tube, no matter what. They're worth some $$$
Of course, anything you can't store for very long, please post a list of what you want to get rid of here and I'm sure you can get people to at least pay for shipping on stuff that you dont want to store... and keep the more valuable stuff and clean/test/use/ebay later.
Trust me.. I'd find room for 100 monitors even if I meant I was parking outside for a few weeks instead of a garage.