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.
Not a lawyer, but my understanding is that once you use a font to create something, such as a banner, what you have is a work and not a font, and the work may be distributed. Embedding a font (as with @font-face) is trickier in that there is typically a restriction in your EULA against transferring a font, which you might have to do if the target server does't have a copy.
In the case of Helvetica it's quite likely that the target server -does- have a license, since Helvetica is ubiquitous. If you are worried, you can always use a similar font (and there are hundreds that look just like Helvetica) that has a more lenient license.