Yes, you can leave jobs off your resume. Your resume is an overview of your most relevant experience and skills for a specific position, not a list of every job you’ve held.
You can (and should) highlight any position that’s relevant to the job you want, while leaving off any jobs that don’t improve your chances of getting hired. For example, any older jobs that aren’t important to your current career path (like a babysitting job you had as a teenager) should be left off your resume.
However, be prepared to discuss the jobs you leave off your resume during an interview. Have an answer for why you didn’t mention a previously held position in the event a hiring manager finds out about it and asks.