Magna-Tiles
Arrange them on the fridge or a magnetic door. Spray with a soap and water solution, wipe, flip, spray, wipe again. Then stack them and spray and wipe the sides.
Legos, Clics, pegs, dishes, and other small waterproof toys
Toss them in a mesh laundry bag and run them through the washing machine on a delicate cycle. Add a towel to the machine to minimize noise and protect the drum.
Alternatively, fill a bucket or tub halfway with warm water, add a small squeeze of dish soap or hand soap and a bit more water to lather it up, drop the toys in, swirl them around, and let them soak for five to ten minutes. Rinse well, spread them out on a towel or some newspaper to dry, and leave them overnight - sometimes longer depending on humidity. Shake and flip them after a couple of hours to make sure water isn't pooling anywhere.
Wooden toys and anything electronic
Wipe with a slightly damp cloth. Don't soak or submerge.
Bikes, scooters, and outdoor toys
Take them outside, soap them down, and rinse with the hose.
Don't have a hose? wash them in the bathtub, using the showerhead to get to every corner
Dolls
Soft and fabric dolls can go straight into the washing machine in a mesh bag on a gentle cycle -air dry or tumble dry on low.
Hard plastic dolls can be washed in a basin of warm soapy water, rinsed, and dried.
Dolls with hair - most good quality dolls can handle gentle shampoo, rinse, detangle while wet, and leave to air dry.
Delicate or porcelain dolls - wipe gently with a barely damp cloth.
Stuffed animals
Most can go in the washing machine in a mesh bag on a gentle cycle. Air dry or tumble dry on low.
Menchies and accessories.
You don't want water getting into the holes.Wipe with a damp cloth and leave to dry.
Puzzles
Wipe each piece with a damp cloth, dry immediately, and lay flat to finish drying before putting them back together.
Board books
Wipe the cover with a damp cloth and dry. For each page, wipe with a damp cloth and wipe dry right away so the pages don't warp.
Did we miss anything? Drop your tips in the comments; how do you wash the toys in your house?