Should I have references on my resume?

Absolutely not. It's not the place for that. Don't even put "References available upon request". It is expected that when the time comes to check references, you will provide them - no need to mention it now.

Here's more reasons why:

• It will make you look bad / out of it - a resume faux pas if you will
• It takes up valuable space on your resume that could be better used for other things
• References are typically only checked after the interview process once a company has decided to hire you (pending reference/background checks of course), so there's no need to include them upfront
• You want to control when and how your references are contacted so you can prep them and ensure they're ready to go / not surprised

If (AND ONLY IF!!!) a job posting explicitly requests references as part of your resume, then fiiiiiiiine. If an application process asks you for them, it's better to create an entirely separate very simple "References" file with your references' names, relationship to you (manager, colleague, client, mentor, coach, etc.) and contact info (phone & email, ideally).