Cannot fit wheel into dropouts I recently bought a wheelset that supports 11sp and 10sp casettes. The wheelset came with a 2ish mm spacer. I have previously owned a 10sp wheelset that had a 1mm spacer.
I have been told that for 10 speed cassettes I'd need both spacers on the new wheelset, so I put both of them on.
It worked for a while until the wheelset developed some (unrelated to this issue) noise so I took it off the bike, but then I  had serious trouble getting the wheel back into the dropout.

Not only did the new wheelset with the spacers not fit into the dropouts, the alignment of the wheelset was off and I couldnt even turn the wheel because it was rubbing the chainstay.
The old wheelset without the casette on the other hand would fit just fine so I thought something was wrong with the new wheelset and sent it back.
Now I wanted to put the old wheelset (which is my trainer wheelset) back on with the casette and only the 1mm spacer.
The problem is that much like the new wheelset I couldn't event get the old wheel into the dropout, so I took out the spacer and it fit first try.
I've used the old wheelset with the spacer in the past and I'm not sure not what I'm doing wrong.
The new (already sent back) wheelset had other issues, but I want to know:
Does this issue indicate a bigger problem with the bike or will I be fine without the spacers ?
What spacers do I need to use with 10sp or 11sp wheelsets ?
What could be causing these problems ?

I have made sure that the length of the hub is compatible with my frame, so that should be not an issue.
You need enough spacers behind the cassette so that when you tighten the cassette lockring there is no play of the cassette on the freehub. Probably 0 on 10 speed freehub, at least 1mm for 10s on 11s FH. The cassette shouldn't touch the frame in either case, so having a spacer shouldn't have prevented you installing the wheel or cause misalignment. If it was the cassette touching the frame that stopped you mounting either wheel there might be scratches to evidence this but it seems unlikely. 

As commented, check that the wheel fits without the cassette fitted at all. Also check that the axle locknuts are tight (i.e. that you can't unscrew anything from the axle with your fingers). Check that there is an even length of threaded axle exposed on both ends (roughly 4-5 mm). 

The most likely suspects in my experience, however, are the springs on the quick release skewer. Presumably you have had to remove the skewer to change cassette spacers. If you put either of these on backwards then they can obstruct the axle entering the dropouts at all, and will cause the wheel to be out of alignment if it does go in, maybe causing tyre rubbing on the chain stay. The springs have a narrow end and a wide end and the wide end goes on the outside on each side. The spring never sits over the threaded axle. There's a picture on http://bicycletutor.com/remove-install-wheels/ 
If you were doing this correctly all along then I'm all out but this might help someone else