I have a 20 year old washer in the garage next to the dryer. In
between them there is a three prong outlet that the washer is plugged
into (the dryer, of course, has it's own).

The plug on the washer is two prong. I always just assumed if it came
that way, it didn't need to be grounded. It wasn't until recently I
began to realize this was a little strange. I can't move heavy things
so I never really have seen the back of the washer until recently when
it was moved. Well, on the back is a wire wrapped up with a little
flat connector thingy that I assume is the ground wire!

My guess is that this was done so if you had a two prong outlet that
was groundable by the plate screw, you would be able to use the washer
by screwing that end of the wire to the screw on the plate. Is that
correct? Is that a common thing (at least back then)?

This is an early '60s house with some grounded outlets, but most not.
Funny enough, the one there is a 3 prong one. So if I connect that
wire to the screw on the 3 prong outlet, will it be grouned?

I'm not very knowledgeable in electrical , so responses in non-techno
babble would be appreciated

Also, how dangerous is having a washer ungrounded?

--
John