This is a dumb question, but I need an answer.
 

I am putting together a rear wheel with a nutted axle, and I need to know, does the washer go on the outside of the dropout? The spacer, cone, and 17mm thin nut don't protrude beyond the cassette - is that right?

Can someone move this to the right section for me please?

Yes, I think, a picture would help

Well, the spacer needs to protrude enough so the wheel can rotate and the chain doesn't rub on the frame in the smallest cog. On every bolt-on axle I've ever worked on, there's been a washer between the axle and the frame.

the 17mm thin nut (locknut) does protrude beyond the cassette. Otherwise you'd be bolting the cassette right onto the dropout.

The distance from the outside of the locknut on one side of the wheel, to the outside of locknut on the other side (or OLD, over locknut dimension) is generally equal to the distance between the inside of the dropouts. Those nuts are flush against the drops when the wheel is mounted.

On the outside, where the nut tightens the wheel onto the bike, there is sometimes a flanged nut, which is sort of like a nut with a built in washer, and there is sometimes a nut with a ridged or serrated washer beneath it. These go on the outside of the dropouts, not wheel side.

You'd only put washers on the inside of the drop out if you were looking to space out the OLD for some reason. Of course if you didn't add an equal amount to both sides you'd have to re-dish the wheel.

On the outside.

Without seeing what you have, I can't think of any time I've ever seen a nutted axle installed without a washer between nut face and dropout face. Just makes mechanical sense, to provide more bearing for the nut, and reduce chewing up the dropout.

Thanks, all. I am going from 5speed to 7 speed, and I didn't account for the extra cogs, so I do need another washer.