My wife and I and one other couple started a "Fine Wine" dinner a few months ago and it started out quite organically. We happened to invite them over for dinner, they brought a couple of nice bottles that paired nicely with the evening's menu and I ended up opening two complimentary wines as well.
The next day, my friend and I both agreed what a fun time it was and suggested holding these more regularly. Now, we have them once a month, occasionally inviting another couple into the fold and alternating whose house we have it at – sometimes it’s just the four of us, sometimes it’s as many as eight. The party's host always sends out the complete menu to all guests at least a week in advance so we know what wines to bring and pair and every couple brings two bottles (essentially one bottle per person for an evening).
They are a lot of fun and not much pressure because we are all good friends. The wives don't know as much about the wines as the men do so my friend Greg and I are really the only two who take time into tracking our tasting notes, etc.
If you want to ensure a casual friendly environment with no pressure, then I think the key is to host them with good friends. I am always more comfortable that way. There are those that will argue that it can also be fun to branch out and meet total strangers that share a passion for wine. I could see how this could be fun but it could also be stressful as there may be a need to "one-up" the other. Check out the "offline events" section as you could probably find some helpful tips there on these types of events. But in my opinion, hosting it with close friends would be the way to go.