Is a bed without a headboard seen as cheap?

If you're worried about appearing cheap, to people who visit your house, particularly the type of people that might judge a person for appearing cheap, and the opinion of that type of person matters to you, then yes, buy a headboard. Or, if this is like a survey and you're asking for everyone's individual opinion, I personally would not judge you as "cheap" for this, but everyone's threshold for these things is different.