Here is the official Facebook link, which states, "You may join up to 6,000 groups." When you hit this limit, you will have to quit certain groups before you may join new ones.
This limit was probably put in place because people were abusing the system by creating groups aimed at spamming people's inboxes. If you get caught doing this, your account could be suspended.
However, it's possible to go over this limit - but you'll need an incredibly large group of fans/followers/subscribers/etc. The way it works is that when you create a group, there is a default limit of six memberships available. If someone wants to be added as a 7th member of the group, one of the existing members has to cancel their membership or else the new person will not be able to join the group.
For example, if I wanted to join a thousand groups on Facebook alone, I would need 600,000 people in my audience to believe in me enough to click "Join Group" for each and every one of those groups. Even if half of them canceled their memberships, I wouldn't be able to add any more members to those groups.
The number of groups you can join directly affects what events you can attend, what pages you can like, etc.
Except for private groups, any user can request to join a Facebook group. The only restriction imposed by Facebook is that a person cannot be a member of more than 6,000 groups. If you hit that limit, you must leave one organization and join another.
That said, most people don't reach this limit because they restrict themselves to only joining groups with more than x members or groups related to something they are interested in. However, if you have exceeded the limit, you will see a message informing you of this fact. You can also view a list of all the groups you are part of by going to your Home page and clicking on View As. This will show all the groups where you are a member and may include some private groups which you haven't joined yet.
It is possible to delete some groups from your account. However, this cannot remove you from any groups you are already a member of. Instead, it will just make you inactive within those groups. To delete yourself from all groups click on "Edit Profile" at the top of any Facebook page. Under "Group Membership" you will find a list of all groups where you are a member. Click on "Remove Me From All Groups". This will place you in a temporary state where you are no longer subscribed to any groups but have not yet been removed from any groups.
Facebook does not establish a numerical limit on the amount of individuals who may join a group, but as a group administrator, you can restrict who can join the group. When your group exceeds 5,000 members, several group functions become inaccessible.
This sort of group is not visible, and the only way to join it is by an invitation from the group's founder or another member. However, due to the large number of people on Facebook, this does not limit the number of secret groups you can belong to.
You can find these groups by searching for terms like "secret" and "group." Or you can browse through groups tagged with the word "secret." You can also find them via specific memberships. For example, if you know someone who belongs to one of these groups, they may have posted a link to it on their profile page.
People post questions about any topic into these groups. Members then answer those questions by posting comments onto the original question and/or each other's comments. These answers are seen by everyone in the group.
Secret groups are useful tools for getting advice from others who have had similar experiences, asking questions you might not want to ask in public, and much more. There are many secrets out there waiting to be discovered!