Mathanxiety's list is great! I would add this more detailed breakdown for toys:
Anything too young for your kids - dump
Anything with broken pieces - dump
Duplicates (where you wouldn't use multiple at once, e.g. keep duplicate matchbox cars, farm animals) - keep one (per child?), dump the rest
Non-matching collections of things like farm fences, or stuff like Mega Bloks + duplo, or 2 different incompatible train sets - keep the one that works the best and you can buy more of - dump the rest
Anything where the pieces constantly get scattered and it can't be used without the pieces - consolidate all - keep a couple of the most loved items, dump the rest. Dump any that you can't find all the pieces of.
Stuff your kids want to play with but always get frustrated with or makes a mess you can't bear to clean up - dump.
Cuddly toys?? Dare I say it? My kids aren't attached to theirs so I cull quite regularly but if yours are, be more cautious.
Watch them playing - stuff that they typically chuck out of the box to get it out of the way and then abandon - dump.
Stuff they are interested in but then almost immediately abandon - dump.
Kits that need adult supervision - pare down to about 3. Dump the rest. Put them somewhere that you'll think about getting them out on a rainy day.
Pens that are run out - dump. Crayons that make a piffling pointless light mark that is vaguely reminiscient of a colour - dump. Keep the ones that are nice, deep, rich colours. Craft stuff to cut/stick etc - consolidate into one container, dump the rest. Encourage them to use it up!
Consolidate toys into containers by type of game - e.g. we have chunky toddler cars (and all people/street accessories), then toy food/utensils/shop stuff, then another for dolls/doctor kit/other adult role play stuff, one for tools, one for mega bloks, one for little tiny cars and same scale street accessories, one for animals, figures and fences. Put a picture on the front (badly drawn, googled, or take a photo) so even little kids can see and understand what kind of thing goes where.
Stuff that needs adult supervision/help AND stuff that has crucial parts which always get lost - put up out of easy reach so they can ask for it, then you know when it's out and can keep an eye that all the bits go back into it when it gets put away instead of just throwing it in any random toy box.
Toys are one thing that you might like to sell if they are complete sets, popular, and you can be bothered to deal with people. But if it causes stress - DUMP!!!! One tip for this if you have a skip is to put a box next to or at the top of the skip with "FREE" written in it and put the decent toys in there - people love a skip and will come and look and this saves the toys in pass-on-able condition from getting wrecked.