"Turn that up!" That's what you exclaim when your favorite track comes on, and that's what you want your audience to say ... in a way ....
You want everyone to fall in love with what you have to share and "turn up the volume" on your message, but you do not want anyone to have to put forth extra effort to actually hear what you say because your voice is not loud enough.
A speaker should always use a microphone. Many will share the sentiment that their voices carry, and that's a great asset for cheering at a football game or the like, but it is not most effective for the public speaking environment. Others have something of a fear of a mic, cringing at the sound of their voice being broadcast through speakers and wanting to stay as far away from a mic as possible.
For a speaking engagement, so that everyone hears your voice at the same volume no matter where he/she is seated in the room, a mic should be used if one is made available. I recommend you always ask well in advance of your event that one be provided for your use.
You should use a mic not only for the benefit of the audience but also for the purpose of ...
... helping to protect and preserve your voice. This is incredibly important if you are a professional speaker and, if you are not a professional, in those instances where you may find yourself having to speak at length or repeatedly in a short amount of time.
Venues that are accustomed to regularly hosting speaking events will likely have lavalier (or lapel) microphones to provide you, which are oftentimes and preferred by most professional speakers as they free their hands for gesturing and/or using a presenter/presentation pointer/clicker to advance their PowerPoint slides. (Some will even have those nifty headsets you oftentimes see musical arts use during live performances!) If no lavalier is available or if the cost is prohibitive, then definitely request a hand-held mic.
What distance should the microphone be from my mouth?
No two voices or miss are exactly the same, but the range of about five to six inches from your mouth is a standard just about anyone can assume. Keep in mind mic volumes and room acoustics will differ, so the best way to determine how well you sound on a mic is to arrange to arrive at the venue where you will present at least an hour before your presentation and request someone from audio/visual be there to check your mic levels. Then ask him/her to be there for the first few minutes of your presentation to make any necessary adjustments because oftentimes, during the actual presentation, your voice will be louder or softer than it is during the mic check.
And if no microphone is present, what is a good way to project my voice so that everyone in the room can hear me?
One of the coolest tips I've found to help with voice projection is focusing on your passion and personality. Seriously. Think about the last time you discussed something that really excited you. What was your energy like? How would you describe your enthusiasm? Was it easy for you to be heard - literally and figuratively? Probably so. When you place yourself in a position to discuss that which matters to you, it's easier for you to speak up and be heard. After you get those two down - passion and personality - ensure you always stand straight, breathe in deeply (but not in a noticeably audible way), and let the air do the work of carrying your sound as you speak.
I have stressed the speaker should always use a microphone; however, are there instances where you do not have to use one?
If the audience is made up of 15 or fewer people, then I would say you can forgo using a mic, and if need be, direct people to please sit in a designated area - preferably toward the front of the room - so you do not have to worry about voice projection.
However, if you know the crowd will be sizable - one that is too large for you to simply use your regular speaking voice and be heard without a mic - then you must insist the coordinator of the event provide you with a microphone. Hands down. It's for both your benefit and the audience's benefit. You do not want to have to strain your voice so as to be heard and possibly interfere with your concentration and the quality of your presentation, and truth be told, the entire audience cannot hear you when you strain nor is it pleasant for the audience to have to sit and listen to someone shout.