Until you start getting sloppy. I went to a beekeeping lecture (/ honey tasting), and the long-time beekeeper said he usually doesn't deal with all the gear, sometimes gets stung but at this point it doesn't bother him much.
More experienced beekeepers start shedding gear. Some only go in with a veil.
That said, some also go in without a veil. This is _not_ a good idea. There was a very experienced (25+ years) beekeeper who told a story at the PA State meeting how he nearly died after knocking over a beehive.
I was helping a friend of the family out once w/ his bees, and he was the kind of keeper that didn't have any veils. I ended up getting stung three times on the same side of my face (twice in my eyebrow, once next to the eye) when they got angry, and I had to leave ASAP and drive 20 minutes home before the swelling would affect my vision.
I was out of commission for about a week after that. The whole right side of my face was swollen, and I couldn't see out of that eye for most of that time. It looked like I got in a fight and lost :)
And that was the last time I went into a hive without a veil.
