There are hundreds of map projections out there and knowing which one to choose for your map can sometimes be a challenge. When choosing a projection, you should consider what your data are showing, which qualities you need to preserve (shape/area/direction/distance), and who your audience is. If you are mapping population density, for example, your map is showing the number of people over a certain area, so you would want to choose an "equivalent", aka "equal area" projection to best preserve area. If your audience is not geography savvy, then a conformal projection that preserves shape may be your best choice because it will make your map "look right". If the area that you are mapping is relatively small (e.g. one U.S. State as opposed to all of North America), you will probably find that there is a projection designed specifically for your area (e.g. a State Plane projection). Your data may also dictate which projection to use - if the majority of your data is already in a suitable projection, then it will be most efficient to stick with that. If you really aren't sure which projection to choose, search the web for maps of your area - you will often find that most of them are in a certain projection.

If you are using ArcIMS, these links from the ArcXML Programmer's Reference Guide are a great help to find the right projection ID and details for your site-config:
Projected coordinate systems sorted by ID
Projected coordinate systems sorted alphabetically
Geographic coordinate systems sorted by ID
Geographic coordinate systems sorted alphabetically

The ArcGIS Desktop Help also has a list of supported map projections, for use in ArcMap and ArcGIS Server.