For years, science has said that the limit is about 150.
Has Facebook - or other social networks, for that matter - managed to change anything? Can the Internet help us maintain more friendships?
An Oxford anthropologist and evolutionary psychologist who is one of the leading experts on those questions decided to take a look.
And for the latter question, Robin Dunbar found that the answer is largely no, even for social media users who friend others freely.
Dunbar, who gave his name to "Dunbar's number" (which refers to that 150-person limit on casual friendships for any given individual) published his findings from a study of 3000 adults in Royal Society Open Science this month.
Dunbar outlines several levels of friendships and relationships in his work.
According to his model, each person can maintain about five people in their support group of closest friends, about 15 people in a sympathy group who are close enough to confide in, about 50 close friends, about 150 casual friends and about 500 acquaintances.
In all, Dunbar's work indicates that any given human can identify about 1500 faces, total.
The numbers aren't exactly the same for everyone. For instance, Dunbar writes that there is some variation in size across personality, age and sex.
Dunbar's recent results indicate that social networks stay about the same size as outlined above, even with the expanse of online "friendships" that are theoretically available on sites such as Facebook.
"The constraints that limit face-to-face networks are not fully circumvented by online environments," Dunbar writes.
So why do "friend" groups get so large on Facebook?
It might have something to do with how social networking sites label connections - most sites don't allow users to sort friends by Dunbar layer.
On Facebook, you can "friend" or "unfriend", even though users with larger networks are actually expanding their "friend" list with lots and lots of acquaintances, Dunbar concluded.
Friendship isn't entirely blind to online connection, however: Although Facebook can't give you more friends, it can help you maintain friendships through online contact that might otherwise deteriorate.
There's one bigger outstanding question here: What about the teens?
But Dunbar says aspects of teenage social media use might support his research findings, indicating that even for more exploratory teens, the task of maintaining large social networks eventually hits a limit.
Teenagers have moved away from using open-ended sites such as Facebook as their primary social networks and instead rely on a handful of ever-changing, more private services, such as Snapchat.