When you are editing an audio file, be sure to cut only at the point the waveform crosses the zero decibels line. Otherwise you can be prety much guaranteed you will get the popping sound you described, particularly with low frequency sounds. You will notice that many audio editors (cubase, Adobe audition etc) have a feature you can switch on called 'snap to zero crossing' to make it easier to avoid precisely this problem.
The trick of swapping the two halves of the audio is a good one for continuous background sounds. I've used it before myself, and what you can then do is crossfade the two halves together at the middle to ensure a smooth join there as well.