Rotating game masters

My versions

As mentioned, my friends and I use a rotating GM system, but we started with a system in which we each not only took a turn being the GM, we also changed the game we played with each rotation. This was usually a weekly change, so one person would have to do a little work for one week, run a one-shot campaign, then hand over the reigns, and play 4-5 other games before it was their turn to GM again.
Our initial setup was done with the idea of not only sharing the workload, which made forming a group more manageable for all of us as none of us have the time to be a full time GM, but we also wanted to try out a whole range of different gaming systems, and we just wanted to learn how to GM. So one week I may have ran a game of D&D, then the next a friend may have ran Dread, then the next a friend may have ran Fiasco, and so on. We played a whole range of all sorts of game systems, and in doing so quickly found our preferred play styles, game systems, and our own GM styles.

This eventually grew into our current system, which is one in which we use a shared story universe, the same game system, the same characters, but we each tell our own stories within this shared story universe. This change came about when we all realized we craved playing a longer campaign, with character we kept for longer than just one game system rotation, and with characters we got to develop and cherish.

Our initial setup was picking a game system (we picked D&D 5e), creating our characters, and creating a shared story universe, which we did using a world building game. There's a decent amount of these games, but we used Microscope for our world building session. After that we were all set to go, and we're still going. Our world is one of islands (they can be sunken, floating, traditional, etc.), each with their own story to tell. Some may be connected, some may be one time only stories, and some might hold secrets we've yet to uncover.

Sharing the load

The biggest reason people go for a rotating GM system tends to be a sharing of the workload. Many people have busy lives, families, and other important reasons preventing them from creating and planning an entire campaign, so cutting it up into shorter bursts allow you to spread out the work of a large campaign over weeks, months, or years.
But there's another advantage that comes with sharing the load, which is that it helps keep things fresh, and prevents the burnout some GMs feel when the workload gets too large.

Collaborative universe building

Part of sharing the load is also the collaborative aspect that comes with sharing a story universe. This element isn't part of all groups of course, as shown by my group's initial setup, but it is one of the possible advantages of rotating GMs.
This is an important thing to consider however, as sharing a story universe requires a certain degree of trust, as well as a willingness to let go of total control. Other players will be able to alter the story universe on their GM turn, so you're going to have to be willing to accept the changes they make and add. A good way of making sure no boundaries are crossed is by simply establishing some rules before the first campaign has even begun.

Even when you don't touch each other's story elements you can still affect them when it's your turn, for better or worse. If you give out powerful objects as loot you may ruin plans of the next GM, if you kill a specific non-player character (NPC) you may end up destroying a secret plot line, and so on. This is all easily avoided by simply marking some elements off limits. If you're worried it might give away which characters or locations will end up being important simply mark some random ones that will never be important to throw off the rest of the group.

Different styles

Another great advantage of rotating GMs is that you get to experience different styles of story telling. Each GM is different, everybody has strengths and weaknesses in their GM methods, so by experiencing different GMs you not only get to experience more, you also have an opportunity to learn from each other, which can only help you become a better GM.
This could also mean having to be open to criticism, so make sure you discuss this in your group beforehand. Giving criticism, whether constructive or not, can be taken the wrong way by some, so don't let this ruin your gaming group.

Story development

One thing that is difficult to manage in a rotating GM system is story development in all its forms. Characters often find themselves in a wide range of locations, some story elements are important one week, but not part of the story of the next week, and so on. This doesn't have to be a disadvantage, my friends and I tend to tell our own stories for example, and we're having a ton of fun. Our stories are still set in the same universe, but they aren't immediately intertwined right from the start.
But it can also be as simple as individual GMs continuing their original story when it's their turn again. Time will have passed in between of course, but that can make for great story development in and of itself. A planet saved from destruction may have developed all sorts of new defense systems, and in doing so gained more power and respect, for example.

Recycle and reuse

If you are looking for a more intertwined universe among all the GM stories, all you need to do is use each other's ideas and elements. It can be as simple as merely mentioning past events, or as complex as expanding upon existing, minor characters. Perhaps a merchant has a chain in the next town, perhaps a previously defeated enemy sends their allies after the group, perhaps the effects of the group's actions have reached whichever location they're in during your session.
This is just one more part of sharing the workload, as you now have a library of existing world elements to work with. A library which'll grow with each session.

On a side note, you could keep a log of all the characters and locations, perhaps in a fancy looking tome, or simply as a single text file on a cloud service. Either way it can make for a great log and memento of the entire overarching story.

Loot & xp

Earlier I mentioned how giving out too strong a rewards could mess up the plans the next GM has. Their monsters may suddenly no longer be a challenge, rewards they may have planned could be obsolete, and so on. So setting up rules for loot is definitely something I strongly recommend. But it goes further than simply giving out powerful weapons. Gold could twist the balance of economies, XP could level up characters too quickly or slowly, and enchanted or magical items could offer the group a way to bypass big chunks of what a next GM may have planned already.

This is all solved by planning ahead of course. Keeping things simple can often work best, especially when you have GMs who aren't as experienced. Level up after each campaign for example, distribute loot at the end of each session, or simply come up with narrative reasons why some gear might not work or be available in a specific campaign.
Alternatively, let the person who GMs next know what items/xp you plan to give. That way they can alter their plans far ahead of time, and possibly offer some changes to fit their campaign as well. Remember, it's a collaborative process.

Playing & GMing

One thing you'd definitely want to avoid is being both a player and a GM at the same time. Your character would have an unfair advantage, as you'd obviously know what will happen next. But even if you don't or play like you don't, the players in your group will likely still think you do know what's next or do try to steer the story in a certain direction, and therefore listen more to your character than they otherwise would.

Being both a player and a GM at the same time opens up a whole range of possible meta gaming elements, which is something most people dislike. The meta gaming elements might not even be real, they could be a simple placebo effect of thinking the GM knows what's up, and therefore following the GM's character. But either way it changes the balance of the game, and usually not for the better.

The easiest way to solve this is to simply make your character sit out your campaign. They may have fallen ill, they might rather spend time crafting, studying, or they might be helping locals not part of the campaign. There's plenty of reasons a character could sit out.
Of course if your character is the only healer or tank, things can get a little tricky. Still, this can be solved by creating one or two shared characters at the start of the campaign. This character will always be controlled by whoever is the GM, but should generally be a background character for the most part, only there to fill in the role of tank, healer, or whatever else your party may need.
A better way is to simply make sure your party is balanced, or to make sure the GMs change their campaigns accordingly. No healer? Bring out all the healing potions. No tank? Bring out the scrolls of magic armor, the softer hitting monsters, or the siege weapons behind or inside of which they can hide.

Replacing characters with items isn't as viable in all game systems of course, but bringing in NPCs can usually help solve the problem of a missing character. The shared character idea adds to the collaborative element, and to the shared universe element as well. But it's definitely important to figure out how you want to handle this character, as some might wish to play the character one way, while others prefer to play it the opposite way.

Player only

Lastly, some members of your group may wish to stick to being a player for their own reasons, don't fault them for that. Being a GM not only requires a time investment, it can also be nerve wrecking to actually run a game in front of a group of people even if they are your friends. So don't force players to GM, nobody will enjoy it. Simply encourage them, offer your help, and be patient with them should they run a game after all. It'll lead to a more positive atmosphere, which is something we all want in a game group, right?