Stay away from Samsung (as KY-Clay & John Alden suggest) and will add LG as an appliance brand to stay away from.
I too like the Whirlpool family of appliances, which includes Jenn Air, Maytag, Amana, Kitchenaid, and Hotpoint, also some Kenmore's.
Frigidaire is worth a look too.
Keep in mind, the simpler the machine, the longer it is likely to last without a breakdown.
That said, The best washer & dryers are Speed Queens, hands down. Even their brochures say they are built to last 25 years.
They only have a few models, and are more expensive than most of the rest, but are absolutely worth it.