At my club we don't have tee times. Never having played at a no-tee-times club, when I joined I kind of figured it might be a source of problems but I've not seen any issues with it at all.
The members have various games with more or less set times although the times vary seasonally. I play in a larger group that goes off about 11am in the winter and maybe 10:30 in the summer. There's a slightly smaller group that plays at 9:30 or thereabouts as far as I know. Also some guys seem to get together around 12:30 or 1:00 but that seems a rather fluid group and time and I'm not sure the details.
The pro shop staff are aware of the usual games and will introduce new members to the various groups as needed. But it's all really managed by the players. Our group has an E-mail list that goes out late in the week to set times for Saturday and Sunday.
The biggest standing game is on Wednesdays. I'm never around at Noon on weekedays but apparently most weeks they have 30, 40, sometimes more players. That's about twice the size of the group I play with on weekends.
As far as I can tell, even the standing groups play on more or less a first come, first served basis. If the course were really busy early on a Saturday, let's say, then we might end up teeing off 15-20 minutes later than we planned. But I think I've seen that happen once in the six months I've been at this club.
There are no doubt "cliques" within the club who prefer to play together but not with others but compared to my previous club it can't be very many people in the "cliques" because I've yet to encounter them. Or maybe they don't exist at all for some reason. This club is very old and has some very long-standing cultural norms that really, truly are inclusive to an extent I've never experienced before. Good players seem not to mind playing with high handicappers, the old guys and younger guys are not quite as segregated as at some places and I've got to say it's the darndest thing I've ever seen in terms of how often people I've never met before will invite me to tee off or join up with a twosome or threesome.
So I guess that's why no tee times work. When by and large the members prefer to join up rather than play alone and given that we are not terribly oversubscribed in terms of membership numbers (deliberate understatement) it just all seems to work out. The culture seems strange to me but I like it a lot!
[ADDED AFTER DAVID WHITMER'S REPLY]
Our club has similar or very slightly larger membership numbers than David's former employer.
And regarding pace of play, don't know about first groups of the day but any group taking more than about 4 hours to play our course generally gets politely encouraged to pick it up a bit. My group are usually mildly frustrated if teeing off around 10 or 11am we end up playing in something like 3:50 or 3:55 but the one time I've seen it it gets up to 4:15 or so was considered highly unacceptable. It's a short, compact course and about 80% of the play is in golf carts (allowed to drive on fairways) so there's really no reason at all to take more than 4 hours to play.
I have no idea of our number of rounds per year.
There is no distinction between women and men in terms of the by-laws of the club. Not sure about younger juniors but teenaged members seem to have unlimited use of the golf course just like their parents, although I think you must have a drivers license to use a golf cart. Many of our memberships are families with more than one golfer who plays regularly. All are treated as "members" there is no primary or secondary status type thing.
We do not employ anything resembling a "starter". Most mornings there is one assistant professional manning the pro shop and signing people in, one lady in the snack bar serving food and a part-time guy that comes in early and takes the carts out of the barn and puts them by the clubhouse for people to use. Other than the greenskeeper's crew, that's it. Did I mention I really LOVE playing at this kind of club?
