Recently I've run into a group of 3.5 players, the majority of which were introduced to the hobby with 3rd Edition (their veteran came in with 2nd Edition). I managed to convince them to let me run a session using rules circa 1981 with a heavy dose of house rules. It was a fascinating experience, which reinforced much of what I believe are the strengths of old school gaming. A few observations:
It was fun. The players very quickly adapted to the free style combat rules and improvised quite a bit (they felt free to grapple, shove, use fire and oil and even tried to use spiked club to jam open a giant frog's mouth to avoid being eaten). We all enjoyed the freedom to be able to try out tactics too difficult or burdensome to accomplish in 3rd Edition. We spent more time describing what we were trying to do rather than crunching rules or rolling dice.
Abstract simulation works. Everyone in the group found combat sans battle mats and miniatures refreshing. It not only allowed the party to move far more efficiently through the dungeon, it allowed for us to take care of entire sequences with a single roll — something that made sense in context, didn't bog us down in minutia, and allowed us to get on with the things we wanted to spend time on.
Old School isn't as random as you think. I didn't allow any Thieves, with the express purpose of forcing the players to talk their way through finding and disarming traps as well as searching for hidden objects and secret doors. The players quickly caught on and each room explored became its own little story as actions were described in detail and rolls were kept to a minimum.
Randomness can be highly entertaining. Old School feels more random than modern games, because games are largely unscripted and often made up on the fly. Those things that do get randomized are non-standard and have a way of creating unexpected events. This forces everyone to get creative in order to deal with the new situation — something that more often than not is highly entertaining.
Sandboxes are cool. The players got a huge kick out of being given random rumors and being allowed to follow up on any that they desired. It was a bit of an epiphany to be allowed to have the goal of the campaign placed in the players hands, as opposed to having the goal being forced upon them by the campaign.
Morale rules work. I used the Maldvay rules for morale and they added a layer of depth to the game even I found surprising. For this group of players, monsters are no longer stupid fodder to be killed by adventurers one encounter at a time. By the way the players reacted to the changing environment of the dungeon as monsters ran away, it was obvious that the morale rule had transformed the dungeon into a living environment that reacted to the players actions. This was no longer a series of encounters, this was a dungeon where danger lurked around every corner.
Jason Vey's interpretation of Vancian Magic is excellent not only for old school games, but for new school players. I ported wholesale the magic system from Spellcraft and Swordplay because it fascinated me and I wanted to see how it played. In my experience, new school players are loathe to play spell casters who get one spell per day and feel that they are done and useless. Vey's system alleviates this to a certain extent, because characters have a chance to cast a single memorized spell multiple times a day. However, there is also a chance that the spell will completely fail (and you then forget it) or won't take effect for an entire round. My players enjoyed these possibilities, it kept spell casters active, and it made using any magic a little bit dangerous.
Simple rules mean you don't waste your time on rules. On more than one occasion these words came out of the mouths of my players: "Simple, I like it!" Instead of trying to look up the rule in one of several 300 page tomes, we made up a rule on the spot that everyone saw as fair and moved on.
Simple rules mean that players can focus on their characters instead of their mechanics. Without skills or feats to worry about, players spent more time figuring out their backstory than trying to figure out how their characters worked mechanically. As play went forward, I also found that the lack of a mechanic actually forced players to role play.
Old School is addictive. The players are already talking about how to fit more sessions into their schedule, because they want more. It goes to show that we old schoolers should be playing our game with those outside our community — the things we love about old school gaming are things that everybody else will see they love, too.