Version 1.7 of QGIS brings substantial improvements in the way CRS and Projections are dealt with by the GUI.

It is helpful to understand some of the conventions which go with the display of shapefiles and their history. ArcGIS (ESRI invented the shapefile) sets the Coordinate Reference System (CRS) for the project from the CRS of the first shapefile opened. Consequently shapefiles created in that project may not have their own .prj file. QGIS has a much more robust system but users may be challenged when externally generated shapefiles are loaded into a project.

QGIS allows the user to control how CRS are managed. The menu item contains two important sub items - Settings - Project Properties and Settings - Options - CRS. You will find QGIS is set to default to WGS 84, but obviously very easy to change.

QGIS uses the .prj file for each and every shapefile and can display a bunch of differently project layers at once, according to the projection set for the project. This is "on the fly OTF projection". Version 1.7 can now do this with rasters, a major breakthrough.

The unexpected behaviour to watch out for;
If you use Google imagery from Open Layers, it will automatically change the project CRS to Google Mercator. If there is unexpected behaviour then perhaps change the layers to WGS 84 projection and coordinate system, and then zoom to layer extents of the shapefiles. The Google imagery is treated as a raster.
Some datasources have other metadata which is incorrect, often when ArcGIS files have an absent or incorrect .prj file. Landsat rasters for the southern hemisphere are incorrectly produced by USGS with metadata which causes them to be projected in the northern hemisphere.
KML files don't have .prj files, depending on what is already in the QGIS project there can be a range of behaviour.

When projections are correct QGIS will display the correct units in the scale bar rendered in the map window. That is to say, if you see a scale bar with unexplained units then a layer is not being projected properly or is not compatible withe project.

Some useful features;
right click on a layer and select the menu option Set Project CRS from Layer would be a good first step for those who are wedded to the behaviour of ArcGIS.
right click on a layer and select the menu option Zoom to layer extents and then see if a realistic scale bar is also displayed, success at this point suggests all CRS feature are behaving correctly.
In Layer Properties - General specify the layer CRS, and also use the Metadata tab to see what it says.
Specifiying the CRS, closing the layer and reopening can fix a lot of problems, mostly by cleaning up someone else or some other software's mistakes.