Only two experienced significant nausea. Two or three more reported feeling a little queasy. The rest didn't have any nausea-related problems.
A few people reported vertigo, one desperately gripping the chair they were sitting on when they looked down. One literally threw the headset off when some VR dolphins in another demo got too close. These are unusual reactions.
I'd say about 90% of the people don't have any problems at all. The consumer Rift should be even more acceptable.
Still, these devices are all in their infancy. Expect devices a few generations in to be far, far better than the ones that mostly target early-adopters today.
I expect the main challenge to overcome for most users will be comfort. Few people will want to wear these things for long, once the novelty wears off. A lot of people don't even like wearing regular glasses. Wearing these bulky, hot, uncomfortable headsets for extended periods of time will not be worth the trouble for most people, once they get over the gee-whiz factor.
Anecdotally, I have a Rift, and do not get sim sickness except in rare circumstances involving at least an accelerating viewpoint, and even then not severely and only briefly.
Motion sickness tolerance varies a lot of course, I wouldn't hazard a guess as to the percentage who would have this problem with VR, but unlike say, watching a color television, the percentage is not insignificant.
As for your discomfort after taking the headset off, this is mostly because current VR tech strains the eyes a bit due to everything always being in perfect focus.
Here's an optometrist having his first experience with VR and talking about what he thinks:
Yes. It's highly dependent on the game, too; certain games seem very prone to issues. For example, The Talos Principle, a first-person puzzle game, causes nausea in enough players -- including me! -- that there's a whole section in the configuration for "motion sickness options", like changing the field of view or disabling head bobbing.
(FWIW, I was able to play through the game comfortably after switching it to a third-person viewpoint.)
Since (nearly) everybody in this thread seems to be under the impression that it's impossible that the vast majority of people who've used the Vive are actually telling the truth about the lack of nausea it incurs, here's one of several weekly videos put out by the developers of Fantastic Contraption, showing people playing their game unimpeded for two and a half hours: https://www.twitch.tv/colinnorthway/v/61979623
In hours and hours and hours of real usage, the only thing about the headset you ever see anybody people in these videos complain about with the headset is sweat.
All entertainment works within some constraints of the medium, and things that are great on one medium often are impossible or just bad on other medium. An expert saying "VR won't work for vehicle/racing sims because of acceleration/vestibular issues" is perfectly compatible with VR working great for real customers - if you look at the provided content, then they manage to provide quite a lot of fun and variety while simply avoiding any vehicle/racing sims, probably because of the same issues.