Honestly it depends on the show. Sometimes I'm very excited and want to see the show ASAP so I'll go to a preview. Other times, if I hear it's being worked on, I'll wait. Or if it's a team I love, I want to see the evolution of it and see the changes they're making, I'll purposely go early and then after opening.
It is often easier to find discounts or comps during previews, though it's not technically cheaper. The list price of tickets is usually the same. I only go back again if I loved it during previews and want to see it again. If I didn't like it the first time, it probably won't be any different. Some shows make little to no changes. Some shows make massive changes. As I said, it depends.
Most of the broadway shows I see, I tend to go in previews. I don't do this deliberately, though. As someone who relies on rush tickets, previews are definitely not cheaper. It's mostly because I see so many shows, that as soon as another one that I want to see begins performance, I like to see it right away. It totally depends on the show, but I have personally found that going to a preview performance isn't THAT much different from going to a regular one. However, there are some cases where I wish I had waited to see it later. Recent examples include Shuffle Along, The Crucible, and Allegiance. But most of the time, I can hardly even remember if I saw a show in previews or after opening.
I usually like the 2nd week of previews or the week of opening if possible. Most of my friends go at those times also and I am able to talk to them about the shows. I actually went to my first preview performance this past season. Would like to have done that for Shuffle Along.
Often times it can be easier to get rush tickets before the reviews are out, or discounts are more readily available, so I go during previews. However, when I hear that a show is being worked on, or "needs work", I'll give a little more time, either til very late in previews or after opening. Or sometimes I simply don't have time during previews and am forced to go later. Other times I'm desperate to see it ASAP.
I guess at the end of the day, it's a combination of what I hear about the show (will it be hard to get rush tickets, does it need work ect), and my schedule and preferences.
I only see few shows multiple times because there is SO much to see, so that's usually not a reason to see a show early. I only go back if I loved it the first time around. I don't really have the time or money to go back to see if a show got any better or just to see if it changed. For example I saw the 2nd preview for It Shoulda Been You (spontaneous and unplanned to go that early), and wish I could have seen it again later because I do think they made some changes and I would have liked to see it again knowing the twist, but it closed so early, and I was still catching up with all the other new shows and I just didn't have the time.
Personally, I feel the best time to go is about a week before opening. That's typically about the time where they "freeze" the show (don't make any more changes) and is typically when the press is coming to review it, so you're almost guaranteed to see the full cast, going full out to give their best performances.
Lately I've been going the first week of previews then I'll go back a few weeks later while still in previews to see what's changed then I'll go back after opening to see what's changed again.
I also love to go the week before opening. The show is usually frozen as critics are in attendance, and I like to see things earlier on so that I can go in with as few expectations as possible. It also makes it fun to see whether the critics's takes then do or don't match my take. Early previews can be tough just because you never know how much the show might still change. I saw Shuffle Along very early and adored the first act but had some trouble with the book in the second--now I desperately want to go back later and see how much work they've done. That's not a "bad" thing. It's just an expensive thing.
Also, I feel like seeing shows in previews CAN be cheaper just in that there are more likely to be discounts and less people competing for lotteries and rush seats. You risk seeing something pretty dreadful, but if you wait, there's also the chance that rave reviews will boost ticket prices and make them incredibly hard to get.
I try not to go the first week of previews, unless there's already been an out-of-town tryout. As Sauja said, discount codes for previews can be easier to find and lotto may be easier, especially if you look before any significant buzz has built. There are more codes and you might see them show up on TodayTix and/or Goldstar.
"This thread reads like a series of White House memos." — Mister Matt
Usually the last 2 previews b4 the opening. Show is pretty well frozen the cast knows what they are doing. Often the week after opening there seems to be a bit of a deflation in energy
If I'm excited about a show, I'll try to see it a couple weeks into previews. I like being "in the know" early on and if I like it and think the reviews will be good, it allows me to snag a return ticket before they come out.
I also think you have a better shot at seeing all the principal actors during previews (though of course people do get sick, etc).
I like to go the last week of previews or the first week after opening. If you go before that, the show may not have jelled yet. So a performance you don't like or a problem in the pace or the dynamics frequently turns out to be something like like or love after the show is frozen.
I believe you should only go to an early preview if you intend to go back.
From my experience, I personally enjoy seeing shows in previews, and then I see them again after their opening. It's interesting to see how they've changed the show, and how it's developing. I had the opportunity to see Newsies during its previews at Paper Mill. I saw it again after it's opening and needless to say, it was interesting and quite the experience. You learn to appreciate the differences before it goes public. And there's a different energy level.