Is it OK to have more than one role in a SCRUM process

Do you think it may be OK for a person to have more than one role in a software development company that wants to use SCRUM?

E.g. is it ok/possible if a person is

SCRUM master and team member
Product owner and team member
SCRUM master and product owner

Which combinations do you think are possible? Do you work in such a team? What should be considered if a person has more than one roles?

Thanks for any hints.

Solution

Thanks for all your answers. I can't select one of them as the accepted answers, because all are valuable. I'm therefore accepting this answer to remove the reminder from my profile page.