My last campaign was a pretty big group. The backgrounds ran from “I am the fourth or fifth son of a minor noble family who decided to leave home and become an adventurer when he found out he could become a sorcerer” to a complex background where the player expanded upon a whole culture of Halflings from the campaign setting book and then set his character up to be a secret double agent spying on a noble household within an evil theocracy. I will say that most were a lot closer to the former than the latter and a couple of people had essentially no background until I asked them for one.
A funny bit, though, was one no background character was getting close to her hometown in game – so, I asked her if she wanted to fill in any details on her family. She then said that her father was a follower of the same god as her cleric and had died as a hero when she was young, but her mother was a frail and bitter and angry woman who resented how close she was to her father. She (the PC) left home a decade ago to follow the calling of her Goddess, and had only been home once in that time to see her sister, with whom she was still friendly with. (Really, only a paragraph then)
Since the mom was frail, I had her as having recently passed away (heh heh heh). The sister that stayed behind was rather rude, though. She became a cleric as well, though, but of a lawful good deity (instead of the PC’s chaotic good one) – the sister said it was because both she and her god believed in “loyalty, duty and honor” – unlike others in the family.
However, the bitter and angry mom was not quite done yet. Her death was just the beginning of her transformation into a lich, who then literally moved heaven and earth in her attempt to get revenge on her wayward daughter. She sent them back in time, then gated in a balor to soften the party up before attempting to kill the party herself. (She failed, but it was a fantastic encounter where the party was in serious danger and both the lich and the party really were down to their last hit points and spells… The lich’s phylactery was also concealed within the now dead body of the lawful good sister.)
I also made use of other backgrounds over time as well, though not always to the player’s detriment like that.
After the campaign, though, the player who wrote the complex double-agent background said that in order to prevent a lich-mom type scenario, he would write a background so detailed, yet so mundane, that it would be impossible for me to come up with anything bad. On the other side, everybody else said that they would go for the “blank slate” background to prevent a lich-mom scenario.
So, I think most types of backgrounds are okay for me as a DM and I prefer simpler ones. However, I think having too many players with detailed and complex background would likely lead to conflicts of interest in game and me to forget to include certain parts of some people’s backgrounds (PC A: Don’t forget, on page 3, paragraph 2, I am from Gilder and we are at war with Florin and my best friend is Prince Humperdink…. PC B: Hey, on page 4, paragraph 4, I am from Florin and we hate everybody from Gilder due to the war and my sister being killed by Prince Humperdink)