What scenarios are better shot with a prime lens? A zoom lens? A macro lens?
Prime lenses are better suited to specific environments - a 50mm f/1.8 is great for food photography, a 100mm macro is quite flattering for portraiture, but neither work well as a general purpose "carry-round" lens. I use Canon's 28-135 IS lens as a carry round, and can't sing its praises higher, even performing well doing some music photography the other week.
My definitions follow...
Prime: fixed-length lens. Shorter ones are good for portraits, while longer primes are better distance shooters than the zoom varieties. You have to use your feet to get the right setup.
Zoom: lens can zoom in and out. Can be versatile, depending on the lens. Tends to have lower performance than prime lenses.
Macro: for closeups of small objects, and sometimes portraits. Not for distance shooting.
I use prime lenses for portraits (e.g. Canon 50mm 1.8), zoom lenses for traveling/holidays and my 100mm macro for well... macro shots :).
I use a Sigma 17-70mm F2.8-F4.5 DC most as it is most versatile. But prime lenses are usually sharper and allow a shorter DOF which is preferrable for portraits.
Whether to use primes or zooms is largely a matter of personal preference. That said, zooms are usually considered to be more versatile and better suited for fast-moving environments--i.e., photojournalism, sports, etc--since you can probably achieve your desired framing more quickly by zooming than by running or changing lenses. When speed is not an issue--say, when making art--primes are great, usually having advantages in size, maximum aperture, and price/performance ratio. Fast primes are a huge asset in low-light situations where flash is not allowed (e.g., performing arts), and/or when small depth-of-field is desirable (e.g., portraiture).
As for macro lenses, well, most true macro lenses are primes. Macro lenses are best for macro (i.e., close-up) photography, but there are macro lenses that also happen to be great walk-around lenses, such as the highly-regarded Pentax DA 35 f2.8.
The correct prime lens will always give the better photos, however owning and transporting 101 prime lenses is not an option for most people, hence a zoom lens is more practical as a main lens.
The other partial problem with prime lenses is that every time you change a lens you risk letting dust in.
The first step to getting a great photo, is to be there with your kit, so ask yourself:
If I use a lot of prime lenses will I be likely to take less photos?