In the few years I've been seriously working on game design, I've gotten to playtesting stage on around a dozen games. In the course of this, I've seen games tend to fall into four categories in terms of what the playtest feels like.
1. It's just broken.
The worst scenario -- the game just doesn't work at all in its current form. This can be heartbreaking when you've got a lot of attachment to the game idea, but it simply doesn't work in practice. I had put a lot of effort into The Fall of Greenland, a "deck destroying" (like deckbuilding in reverse) game with a viking theme. It ended up simply not being fun. I did three or so playtests, trying to massage the rules, but in each case it fell into the same trap: each player's turn was a small puzzle-solving exercise (half of the time obviously impossible). There wasn't anything in the way of longer-term strategy, or even short-term tactics. And the player interaction that was supposed to enrich the game was unmotivated. Usually the only thing you can do in such a case is toss the whole thing out. I'm still attached enough to the idea of a viking-themed deck destroying game that I'm not throwing it out yet, but I know it's going to need a fundamental rethinking of all of the core mechanics to turn into anything playable.
2. Churning Your Wheels.
On the first try, the game doesn't work. So you change some significant things -- and now it fails in a new way. You change it again, and it finds yet another way to fail. This was my experience for a while with Dinosaur Hunter, a mod of Monopoly in which Atlantic City is overrun with dinosaurs. The mechanic for moving the dinosaurs went through at least four different iterations before I finally hit on something that was quick, interesting, and strategic, while also affording enough movement in the dinosaurs to make hunting them and protecting your citizens both worth it. So games in the wheel-churning situation can be improved, but it's a very frustrating experience. Wheel churning can also set in later in the playtesting, in which case it can be even more frustrating. You've got a basic idea that pretty much works, but you're not quite hitting on the changes that you need to make it all come together. When you've put in that much work, it's hard to walk away.
3. The Hole in One.
This is the kind of playtest we all hope for. You play the game for the first time and it just works. It's fun, it's balanced, it keeps everyone engaged. This is what happened with my current top project, Warm Kitties. After the first playtest, the only changes I made were to shrink the board by a couple rows, and to make a new physical mechanism for the worker placement system (which didn't change the game mechanics or strategy, just eliminated annoying upkeep tasks). But I placed this type of playtest third, rather than last, because it can be deceptive. The game works so well that you assume it's all locked down. You stop looking at ways to improve it because it seems fine as it is. With Warm Kitties, for example, it took me a long time to actually implement the shifting light and shadow that playtesters had been suggesting to me from the beginning, because the game worked just fine without it.
4. The Steady March
The most satisfying kind of playtest is the steady march. The game may start out broken, or boring. But with each iteration, you can feel the improvement. Each time you play, it gets more fun. That's the situation with the current main project of my game design partner Jasmine, called Cool Table. There were too many pieces on the board, so we eliminated some and it worked better. The card-selling mechanic encouraged hoarding, so we switched to getting money for forward movement -- solving both the existing problem and another problem of over-focusing on a few pieces. You get more excited about working on a game and playtesting it a lot when you can feel the improvements actually happening.