Habitat for Humanity takes some, but their specifics vary by branch. I think their website has information.

We also used Habitat to donate many parts that we were not able to re-use. In addition to appliances, they took light fixtures, cabinet doors, wainscoting, shelving, closet doors, knobs, etc.

If you don't have luck with your local Habitat branch, you might try a church, community center or other non-profit in your area. If they can't take it directly, they may know a family in need to connect you with.

Our W/D went to a member of the contractor's crew, frig. and old freezer went to a community center and oven went to Habitat. Although none of these were pretty, they still had some life in them and I was glad they did not end up in the dump quite yet.

The church is the best way to donate stuff. You'll be sure they'd be given to the needy and not resold at all. I heard some charity house sell them. That's not charity if the money won't be distributed to the needy.

My local Habitat is extremely picky about accepting appliances. Mine were just too old for them. The cooktop and oven were on a death watch anyway, so they took the short trip to the landfill. I gave the old dishwasher to a friend who owns rental property - she likes to have a few cheap spares on hand for emergencies.