I have a love/hate relationship with most laundry baskets. They hold and carry stuff really well, until...
These aren't the super cheapy cheap baskets, either. I think the big ones are currently $10 at Target - not super high end, but I had hopes that they wouldn't disintegrate with normal family use in less than 2 years. They're 2 bushel size, after all - they're supposed to deal with the weight!
So the last trip I made to IKEA, I found that they had added flexible rubber tubs to the laundry area, calling them laundry baskets. They were only $5, and I was down two good baskets at home, so I bought two.
See those handles? They're actually pretty beefy.
And it's flexible! See how it bends?
They carry a good amount of weight, even though they're about half the size of my old laundry baskets, and the compact size makes me feel less like I'm going to scrape my knuckles when I walk through the door. If I found myself in a spot where I had to hand wash my laundry again, they'd make pretty reasonable washtubs, or I could fill them with ice and drinks for a party.
Of course, not everyone is near an IKEA, but rubber tubs are available in lots of stores in the summer. The handles might not be as nice, but the tubs will avoid the cracking and pinching problems so common with regular baskets.
On the IKEA laundry topic, they also make my absolute favorite drying racks, the FROST racks. They're only $15, fold to less than two inches wide, hold a full load of laundry, and don't have the problem with overlapping clothes that you get with the usual accordian-style racks. They look flimsy in the pictures, but they hold sopping wet jeans and towels without bending - they're tougher than they look.
No affiliate links here - I doubt IKEA even offers an affiliate program. Just a fan.