Because I primarily design wargames, most of my designs are for two players. As a result, the structure of the game is usually a series of alternating player turns or impulses: player A then player B then player A then player B and on and on until one of you wins. Now, there's usually a little more to it than that. In the Shields & Swords II games, for example, it's possible for a player to take two turns in a row, while the initiative roll in Supply Lines determines which side goes first in a given Game Turn. But as a general rule of thumb, if it's not your turn right now, it'll be your turn next, and you're not at any particular advantage or disadvantage because of whose turn comes before yours, or after.
Multiplayer games - by which I mean specifically games that seat three or more - can be a different beast altogether. If you've played the game Puerto Rico, you're probably familiar with the game's dominant strategy: sit to the left of the new guy. The short version for the wargamers in my audience is that on your go, you choose a type of action, which you perform with a special bonus, and everyone else gets to follow that action. Inexperienced players often choose actions that are more helpful to their opponents than to themselves, or that set up the next player to take a primo extra-special action on their turn. Kevin keeps taking Craftsman so Bob keeps hogging Captain and gets that sweet bonus and by the time it comes around to me I'm stuck with something lame like the Mayor. (And, you know, I'm not really mad at Bob. If my turn came right after Kevin's, I'd be Captaining the heck out of the thing.)
So the argument can be made that it's a game whose outcome can be pretty dependent on seating order, and that can be seen as a flaw. Certainly I've heard folks knock the game for that reason: if where you sit at the beginning of the game dictates what opportunities will be available to you, why bother to spend a couple of hours playing the thing out? Especially when there are games that don't have that problem?
Sticking to the euro crowd, Power Grid is a good example of a game where seating order doesn't matter, but turn order very much does. Every turn, the turn order is redetermined, and generally speaking the player who is furthest ahead will go last in most phases, and the player who is furthest behind will go first. A key part of good play is knowing when and how to manipulate your place in the turn order, so that you have access to the best builds, the best resources, and the best power plants.
When I thought I was a eurogame designer, I went in for all sorts of ornate turn order mechanisms, where this phase went forward and this phase went backwards and this one started in the middle and wrapped around, all with the goal of avoiding the Puerto Rico problem where seating order dictated viable strategies and their outcomes. Probably a little too ornate, now that I think about it - a little too infatuated with its own curlicues and flourishes. In retrospect, I'm kind of glad they didn't make it out into the world. After all, if I had trouble remembering what phase went which way, goodness knows if players could make heads or tails out of it.
The first multiplayer game of mine to get published was Northern Pacific, which essentially uses seating order. To be more accurate, you shuffle a wee little deck of turn order cards, and the player who gets the number one card goes first, the player who gets the number two card goes second, and so on. Players who are so inclined can re-seat themselves so that number two is clockwise from number one, and number three from number two, or they can sit there staring at their little cards and continually ask, "whose turn is it again?" - hey, you do you.
I bring this up because Northern Pacific manifestly does not solve or avoid the Puerto Rico problem. In fact, in a way, it is the Puerto Rico problem, and only the Puerto Rico problem, and it never gives you anything other than that: it's all about who has the turn immediately before yours, who has the turn immediately after, and which folks have turns in which order before it comes back to you. The game's decision space is all about constructing (and derailing) giant chains of if-he-does-this-she'll-do-that-which-means-I-should. I could have called it Turn Order: The Game, though I think Rio Grande would have a tough time selling that one.
Creating Northern Pacific very much helped me become more comfortable with that aspect of Puerto Rico, to the point where my principal discomfort with the game now is the way it not only fails to engage with, but indeed purposefully glosses over, its historical theme (but that's a discussion for another time). Who-sits-where isn't a bug, but a feature, a part of the decision space to be grappled with.