can I connect a microphone to the iPhone?

No, the iphone does not have the functionality for that.

If your iphone is hacked, then further discussion is against the terms of use of this forum.

Since the iPhone has no USB port, it will not be possible to connect any USB device. The iPhone can accept an external microphone through it's audio port, but at this time there is no functionality for doing recordings. Whether or not that will become available in the future, either from Apple or from a third-party developer, no one here can say, but I'd wager that there is at least one developer somewhere who's at least trying to make such a function available. We'll just have to wait and see.

When I record the greeting for voicemail... that is not done on the iPhone itself, but by contacting AT&T ???

No, the voicemail greeting is recorded by the iPhone.

There is a mic available for the iPhone. It's made by Griffin and it is for Karaoke purposes. A mic would only be useful when it comes to record your personal greeting in voicemail. therefore, I don't use the one I own with my iPhone. I do use it with my iPods though. It's great for funning. The only issue is the feedback. Check griffin.com for more information.

The original poster was, unless I misunderstood the question, wants to be able to use the iPhone as a portable recording system (like the small digital dictation devices), something which isn't today possible. Recording a voicemail message is different, and is of course possible.

see the new 2.0 app called "VoiceNotes"

I purchased QuickVoice $9.99 from the iTunes App Store. It works fine, but it's no iTalk, like the iTalk availble for iPods from Griffin. I was able to record a 55 minute lecture, with fair quality. I think the real limitation is the surface area of the microphones and the distance the speaker is relative to the iPhone position. However, converting the iPhone 3G or iPhone running OS 2.0 into a Digital Voice Recorder is possible. I also seen a $4.99 as well as a FREE application that will do variations of the same thing as QuickVoice. -- Good Luck