To start, as most other people do when they first get into the world of Table Top Roleplaying games when they are younger, all of the "missions" as I called them on the time where so very linear. The players would start in one place, be told they needed to go here, complete this job and come back for some sort of reward. Over and over, this process would take place. And at the time, that was great. The players where enthusiastic, they loved these "missions" I would come up with.
And this was all good and well. Till we started to get older and the players wanted more "Freedom". Ah... that word can be a double edged sword cant it? The players had begun to feel what I call "Railroaded". These particular kinds of games are incredibly linear. Where the GM has one set path that the players can fallow, and there isn't much room for them to budge when it comes to what they can or cant do. For a few players, that's alright and is just what they are looking for. Though most tend to find this type of game very annoying.
Players have these grand ideas in their minds of what they wish their character to do with their lives. And it can be very hard to accomplish this goal with their characters, or the "Perfect Moment" as I call it, when you are set on a straight path with no breathing room. So over time, I gradually allowed the players more freedom to do what they wanted. Though in order to do this, I had to become more ready for anything they may chose to do that I hadn't planned on, creating more work for myself in the end, but a more enjoyable game in the process for everyone.
Eventually my games evolved into what I now call an "Event Based" adventure. Where the players would accomplish a task ahead of them, and depending on how they went about doing it, it would cause another "Event" to take place. This allowed for quite a bit more freedom for the players to go about the tasks at their leisure and over all more enjoyable for them. They could move from place to place doing small minor tasks with no time restraint and could hold off on the main "path" of the adventure till they felt they where ready. The down side to this, is that the game can very easily get side tracked from you originally had planned, and take complete new directions that you just are not ready for.
Taking the game even a step further towards character freedom, is an all out "Sandbox Game". Now this term can be viewed very differently depending on your experience with it. For me, a Sandbox Game is where you set a world out before your characters, such as Eberron, and let them at it. They move from place to place as free as they like and have to drive the story forward themselves, as there are much less plot hooks thrown at them than any other game type. While not having to plan out as much of the game, you may still need to plan major events that may take place at a certain time, and you need to be very "quick on your feet", otherwise the game can get bogged down and boring for the players when much isn't going on.
Now, some of the major issues that I have come across with players through my GM career all come from these three various game types, and are as fallows in no particular order:
Lazy Players: Ah... my most dreaded issue with players. I have found over the years, that some players wish to have everything handed to them on a silver platter. They want plot hooks thrown their way, all the information they need to come from a single party that approached them, lots of hand outs be it magic items or money... and they just wanna kind of go along for the ride.
There is another variation of lazy players that I find common. Those players who want to have the "Freedom" of a sandbox style game, but don't want to ever have to go out looking for the action, and wish it to come to them. This can be very difficult to deal with, as this problems comes up for many different reasons. In my experience, the most common cause of this problem is lack of interest.
Do your players find your main hook or story line interesting? Because if they don't... or if they lose interest, that can stop their enthusiasm for your Sandbox style game dead in its tracks. When recruiting for this sort of game, make it very clear that it will be a very player driven game. Sure they will have an ultimate goal put before them, but how they go about accomplishing that goal is completely up to them. They will need to take the initiative to get the job done. This does not mean there will be lack of GM participation for any period of time. There is always something a GM can be doing.
If you feel that your Sandbox style game is bogging down due to lack of interest, be frank and forward about the issue. Ask them why. Never feel afraid that you will seem like a bad GM for asking your players how you can make the game more memorable and more fun for them. That's simply untrue. Be pre-paired for some criticism, because you will get it, but don't take it to heart. Learn from their suggestions, and make yourself a better GM so you can have more fun in the games you run.
Defiant or Disruptive Players: These are a duesy. This kind of player goes out of their way to make your life a living hell when it comes to trying to GM your games. They will do whatever they think it is, that you don't expect them to do to try and catch you off guard. (As Viletta Mentions below, this can be a very good quality in a player. I am more targeting those who do these things simply to cause problems in the game. Such as deciding its a good idea to out of no where trash the building of the person who hired you for a job, simply because they "can". I will add a few more examples when I think of them, as I am drawing a blank right now.) They may try to abuse your system of doing things. They may even attempt to cheat. This is not a very common problem that I have seen on these forums, and have never had the "pleasure" of having someone like this in any of my games here.
There are two ways of dealing with this sort of player. First and foremost, contact them in private, and and try to politely ask them why they are doing what they are doing and ask them to stop. Many more times than not, they may try to claim,"Well that is what my character would do." No... that doesn't work. Yes, I understand that your character may take on a life of their own, have their own personality separate from yours and "Be their own person". But you still have ultimate control over your character, and this sort of behavior is simply un-acceptable. If that does not work, remove the character from the game. Having one less person is better than having someone slowing down the game and removing the fun from it for you. Cause remember, we are all here to have fun. Including you, the GM. Trust me, there are many, many other players out there that will make a suitable replacement.
Rules Lawyers: I loath this sort of player personally. There is nothing more aggravating to me, than bogging down a game over some sort of rules argument. Most of these players tend to be this way, because they want to be able to bend every rule and take every loop hole when they can to give them an advantage.
Before you say anything... to me, a Rules Lawyer is not someone who knows the rules very well and understands how to present those rules to better the game. A Rules Lawyer is someone who knows the rules very well, including mis-wordings, loop holes and the like and presses their opinion of the rules on other players to gain an advantage and interject themselves as simply being better, because they know the rules so well.
Dealing with a Rules Lawyer is very different in a PbP game than at a table. When sitting at a table, It is my number one rule that all GM rulings are final, and should you have an issue with the ruling, bring it up after the game as to not slow down its progress. In a PbP game, I like to set aside an OOC/Rules Discussion thread just for this purpose. Don't like a ruling? Bring it up there. Like to discuss the rules in general while the game is going on, bring it up there. Rules should never... ever... be brought into the actual game thread.
Another way of dealing with this sort of player is to make sure that everyone "Checks their ego at the door." Everyone who plays these sorts of games, tends to be more mature than others in various ways. Everyone should be able to set aside their differences, and be respectful to one another. Discuss rules, don't explodingly argue them. Its childish and makes you look like an idiot.
These are the three most common issues with players that I have come across. I am sure there are many more, and perhaps if you have some insight on the issues, you could lend us all a hand and tell us of your experiences and how you personally deal with these issues. We all will always have something to learn. Remember to keep your eyes and minds open, as our players will all teach us very valuable things. The second we stop learning from them how to be a better GM from them, is the second we have failed. Thanks for reading, and I hope you liked it. Take care.