Craters and Freighters will collect, crate/wrap and ship appliances. But they are franchise outfit and aren't located everywhere in USA. You can go to their website and search if they service a particular area where you need something collected. Beware C&F are not the cheapest option out there, but provide consistently good service.
Next option would be UShip which is like eBay for shipping. Using their website you can set up something that needs collecting/shipping and to what destination and how (crate, blanket wrap, etc...), then wait for shippers to place bids.
Not all shippers on UShip will crate or pack items. You need to spell out exactly what is required up to and including if seller or whoever has item currently will be involved at all in process. That is if there is a washing machine and dryer in someone's basement and current owner won't be lifting a finger, then all that must go in Uship listing.
Many of us here in group have used either Uship or C&F; it varies by what needs collecting and other situations. Again if you have an item that needs to be crated and packed securely going with UShip may make more sense than C&F.