Just a quick point to note here is that if you have (in the theoretical world) a true harmonic vibration then you will see the same vibration level no matter which radial direction you are taking the measurement.
However, we know that differing causes of vibration give a resultant that is often direction specific. As almost everyone here has stated, it is best to take the readings in 2 radial directions but much more important is to be repeatable - make sure you always take the readings at the same place. Personally, I always try and take one reading in the load zone (thanks Ilangford) and at least one other as close to the perpendicular to the first reading as possible.
The practice of taking readings at 45' appears to have started with the gas turbine and centrifugal compressor community. This was done so that true orbits could be taken of the shaft using the built in displacement probes without having to worry about the gravitational effect on the shaft. This works excellently for checking alignments with vibration as well as looking for shaft whirl, rub or even a rotating stall on a centrifugal compressor element.
My point, Kashnap, is don't worry too much about convention when you are taking readings with a portable vibration analyzer but use your engineering experience and good old common sense.