Can I use Helvetica if I have a Mac? Since Helvetica comes with all Macs, and I have bought a Mac, does that mean that I can use that font commercially? For example in a banner or website header?
Yes, buying the OS includes the license to use these fonts in derivative work, like graphics, even for commercial applications.

You can however not redistribute the font in any way. Font embedding in websites through the @font-face CSS feature for example qualifies as redistributing the font (even if it is in another format), and requires a seperate license.