Do people sometimes accuse their partner of cheating because they are doing it themselves?

Sometimes they do, and sometimes cheaters don't accuse their partner of anything.

Yes, it does happen. My first wife did it to me all the time and it turns out she was cheating.

It was accusations over trivial things. When she did what was considered 'worser' things like socializing with male friends (which I met and got on okay with them. Also, they were friends with her before I got with her) and I was perfectly fine with it. But she would have had a problem with me doing such things. Double standards.

I think it happens a lot. I have even many partners go through accusations only to find out the accuser was in fact the cheater. But sometimes people can be wrongly accused because that's the paranoia of the partner.

I don't think either scenario applies in every case though, but possible it happens a lot.

Yes, it is very common.