My wife tried something like this when we moved. I laughed it off. She then suggested I put the collection on shelves in the garage. I laughed that one off, too, then bought a couple thousand dollars in shelving for the new place. I don't think she really grasped the significance of the stuff to me before that.
I've thought about these kinds of scenarios a lot since then (haven't we all? ...no, really - haven't we all idly considered these at some point?). I've even done a bunch of paring down, though that's not really saying much - the collection is still large.
Part of the trouble for me is that I'm also a boardgamer, CCG player, PC video gamer, and miniature wargamer (minis and terrain, in particular, take a lot of space). Balancing limited storage space against all of these is tough.
Anyway, back to the OP's question (or nightmare scenarios, if you prefer)...
1) You only need to trim. Say maybe a quarter of your current levels. What would go? How do you prioritize?
The question is simply: what wouldn't I miss too much? For me that means several DP9 games I only picked up 'cause they were cheap (Gear Krieg and Core Command; got 'em nearly free), the Witch Hunter: the Invisible World stuff (nowhere near as good as I'd hoped), the remaining Rifts stuff (remaining because I culled this a year or so ago - and, as others have mentioned, you can't pay people to take it), the AD&D 1E and 2E Forgotten Realms stuff (I have a greater fondness for several other AD&D2E settings). Lastly, all but 1 of TSR's Amazing Engine books, keeping Bughunters, which I have always been inordinately fond of. This should put me in the ballpark. If there needs to be more, it'll be the D&D 3.0 material other than the core books, but don't be fooled: I have a lot of 3.5 material.
2) About half needs to go.
Now you're talking seriously difficult decision territory. All of the above, obviously, but my AD&D 1E core books go under the knife (I'd keep a number of the modules; I like modules and run them or plunder them regularly now). The DP9 stuff tossed earlier is joined by the Heavy Gear 3rd edition material, plus most of the 2nd edition colony and space-based books. The White Wolf D&D3.x Ravenloft run, which I really want to like more than I do (the setting is just ill-suited to the 3.x system). Palladium Fantasy and Robotech fall under the axe next, followed closely by MERP (except the Northwestern Middle-Earth Gazetteer; great for any Tolkien RPG!) and Rolemaster, plus all but Fell Beasts & Wondrous Magic and the revised core rulebook for Decipher's Lord of the Rings RPG. AD&D2E's Al-Qadim setting stuff would have to find a new home (I'd keep the Arabian Adventures softcover book). All my Pathfinder RPG stuff (other than miniatures, that is), including some 3rd party books like Slumbering Tsar and Tome of Horrors. I'd cry a little bit as I finally got rid of my MSH and AMSH stuff, even though it's been superseded by ICONS for me.
3) 3/4 needs to go.
I have difficulty imagining this under all but extreme duress. The D&D Basic stuff would have to go, along with all the clones save ACKS. Virtually all the D&D3.x settings and supplements (Forgotten Realms, Majestic Wilderlands, numerous Necromancer modules and boxed sets). The small amount of Traveller stuff would suffer a catastrophic mis-jump. Warhammer Fantasy RPG 1st edition stuff has to go, along with the new Advanced Fighting Fantasy. The AD&D modules I held on to from before. DP9's Tribe 8 and Jovian Chronicles would be shown the door (but Heavy Gear can stay). I'd probably keep my AD&D2E core books, plus the Complete and DMGR line. Planescape, Dark Sun and Ravenloft would still occupy a bunch of shelf-space, although a little less than before. In reality my AD&D2E stuff is close to a quarter of my collection on its own. The D&D3.0 core books (PHB, DMG, & MM) plus Ptolus would stay; I could get years out of those (yes, I know the editions don't match; I like D&D3.0 more).
4) Really drastic. You can only keep a small backpack full of games, so figure 3-5 books and some dice, etc...
Why don't you just cut my arms and legs off while you're at it? Hmmm...this is basically desert island stuff. Here goes: ACKS, Heavy Gear 2nd + Life on Terra Nova, Call of Cthulhu 6th, ICONS, TSR's Bughunters. Then just shoot me once you tell me one of these is one too many.
Every time I consider this type of masochistic fantasy scenario, I'm reminded just how true the following is: you don't own your possessions, they own you.