My most favorite random encounter was when I was in an area where Fiends, NCR, and the Legion could travel... It was off by that George guy near the Boomers' Air Field. In this area, there are multiple mattresses with wastelander drug addicts... At that time, i had been hated by the Legion AND the NCR. Since i was a high level, NCR veteran had came up to me and threatened to fight, I let my companions attack but about five seconds in, 5-6 legion troops come in and pick a fight with me!! So now i had both factions fighting me at once... another few seconds had passed, and 7-8 fiends with plasma blasters had came rolling along and started shooting without coming up to me. Fortunately, this trigger the NCR and the Legion to fight against the Fiends and then each other... I slowly backed up and watch the 3 factions fight eachother, ending with The NCR on top...
Their Rangers and Veterans are indeed a good challenge..
*btw i was even more hated by the NCR and the Legion too damnit
Post your favorite random encounters too!