It depends on your needs, wants and budget.

Here is the short list:

Most Reliable/Best Build Quality:

compact front load: Miele

Top Load: Speed Queen (Classic Model)

Both of those recommendations are at the top pf the price range.

27” American Size Laundry

LG

Whirlpool

Those two will be the most reliable based on the review sites and forum posts that I have read. They wont be as pricy as the top picks, but the build quality is lower and the service network will be hit or miss. Based on their price point most major repairs will be more than many people will want to spend. This, most likely by design, will mean the appliances are disposable once the warranty expires.

So you either pay more up front for a more reliable appliance or pay more often for a less reliable one.

Which Brands Make the Most Reliable Appliances?

@luna123456: "This, most likely by design, will mean the appliances are disposable once the warranty expires."

By luna logic, nobody repairs his appliances and every appliance that breaks after a year, the typical warranty period, is thrown away. Yup.