I personally never use one (even on a Windows computer).
For Android, I ONLY ever install apps that are in the play store, and even then, I carefully look at the permissions required, etc. If you are installing apps from outside the Play Store, then I'd say, yeah, use an Anti-Virus app, especially if you are acquiring the apps from questionable sources. But, if you strictly are installing from the App Store, and you have Side Loading turned off, then I'm not sure it's required, since Google also scans for malware.
So, as a few other people said... sometimes just a little common sense will do more than the Anti-Virus software.