Here is my thinking …
Resumes are essentially marketing documents. Their main purpose is to present your relevant experience and qualifications to an employer that (hopefully) will get you to the interview.
Resumes—first and foremost—must be truthful and should not mislead the reader in any way. Having said that, I do not believe you have to include all past jobs you have ever held on your resume.
For example, you might leave a job off your resume if:
The job is dated. Some people include every job they have held since entering the work force. Even if you are mid-career or beyond, a new employer will only be interested in what you have done over, say, the past ten or fifteen years.
Your time at the job was brief. If you worked at a job for less than six months and it is not directly related to the job you are applying for, you might leave it off your resume. Leaving it on could raise questions about why the job did not work out for you.
Your work was part-time, short-term, or contractual in nature. A number of people do term work while seeking full-time employment. It is not necessary that you list all these roles. However, if you wish, you may group them under one heading called “Contract Work” which signals that you were not sitting around doing nothing for a period of time.
You took the job simply to generate extra cash. A short-term job that helped you pay some bills while you sought full-time work can likely be left off your resume.
Having said that …
You should never omit relevant jobs (or any information) from a resume that will cause an employer to be misled in any way.
In particular, you should never omit a job to hide bad experiences. Even if you were fired from the job or left on bad terms, you should still include them on your resume.
Leaving them off will undoubtedly backfire on you.