Indeed, that was the recent predicament reportedly facing Bill Gates, the chairman of Microsoft. During an award event this week in India, Gates admitted to the gathered crowd that he had deleted his Facebook page because managing his friend requests had become "way too much trouble," the BBC reported.
Gates -- whose PR reps didn't immediately respond to ABC News' request for comment -- didn't clarify whether he was referring to a public page or a private profile, though since he referenced friend requests he was probably referring to a private profile. If it had been a public page, he wouldn't need to manage the incoming traffic from wannabe friends.
"With a Facebook page, celebrities do not have to 'accept friend requests' but instead can connect with an unlimited number of fans and foster real-time conversations with them," Brandee Barker, Facebook's director of communications, told ABC News via e-mail.
Gates' departure from Facebook, however, doesn't mean that other celebrities are jumping ship, too. On the contrary, the popular social networking site still boasts an impressive roster of athletes, entertainers, politicians and other public figures.
With Facebook's help, we've cataloged here the 10 most popular celebrities, as determined by the number of fans following each celebrity.
Michael Jackson is Facebook's most popular celebrity. With 10,018,585 fans, the King of Pop is comfortably ahead of his closest contender, President Barack Obama, by nearly 4 million fans.
According to a Facebook spokeswoman, the King of Pop's page has benefited tremendously from a giant posthumous bump, with its fan base rising from 800,000 the day before Jackson's June 25, 2009, death, to more than 12 times that at its present size.
Jackson's page includes previously unavailable music videos, and, in the buildup to Jackson's memorial, it updated fans on the latest news surrounding his memorial service.
In winning the 2008 presidential election, Obama secured the support of more than 62 million voters, but on Facebook, the leader of the free world could only manage roughly 6.5 million fans, still enough to make him the site's second most popular celebrity.
Organizing for America updates his site frequently, informing fans of press conferences, television appearances and other important events ongoing at the White House and around the country.
Obama's status bar informs readers -- in case they haven't been paying attention -- that "President Barack Obama is the 44th President of the United States of America."
Ask a few people to name the world's three most famous people and chances are their answers will include Michael Jackson and Barack Obama, the two most popular celebrities on Facebook.
But only the most devoted fans of the "Fast and the Furious" film franchise would include in that list Vin Diesel, Facebook's third most popular celebrity.
The action film star may not be a pop icon, or presidential material, but he has drawn a stellar following of more than 5 million fans to his page, which he updates frequently with photos, status posts and video clips.
It should come as no surprise to learn that Megan Fox has earned her place on a popularity list.
The Hollywood vixen has attracted rabid devotion ever since she graced the screen as the starlet of the blockbuster film "Transformers," her sultry magazine poses and her provocative quotes.
Fox has nearly 4.5 million fans on her Facebook page, and she honors their dedication by adding glamour shots -- albeit infrequently -- to her page. (Not that there's any shortage of photos on her site; fans have added 975 of their own.)
Will Smith's Facebook wall may be slightly bare, but he more than compensates by chocking his profile full of songs, videos and photos. The former TV actor turned rapper turned movie star has more than 4 million fans on his page. Notable among the videos are personal messages from Smith, including a Fourth of July shout-out to his fans.
Say what you want about Lady Gaga's bizarre fashion sense, the lady knows how to draw fans to her Web site. The 23-year-old glam-singer has almost 3.5 million fans on her Facebook page.
Lady Gaga posts about her music career, informing readers about her upcoming tour dates and progress in the studio, and also offers fans the occasional sartorial tidbit.
And, just in case her fans worry their devotion to the singer is unrequited, Lady Gaga dedicates status posts to her fans.
"In every minute of the day, the truth is that I'm dead, until I'm here on stage, with you, then I'm alive instead," she revealed in a post.
Adam Sandler has made a career playing the "Average Joe" character in his movies, but he's certainly breathing refined air at the top of the Facebook summit. Sandler, who stars in the upcoming comedy "Funny People," has accrued roughly 3.3 million fans on his Facebook page.
His page is full of videos, interviews, photos and movie clips, and includes a brief biography under the info section, which may help fans learn more about the popular actor.
Ashton Kutcher is no stranger to the viral community. In 2009, the 31-year-old actor and former model became the first Twitter user to surpass 1 million followers, eking out the news network CNN, whom he had challenged to a Twitter popularity contest.
It's surprising, then, that Kutcher doesn't have a larger following on Facebook, though his nearly 3 million fans are still enough to put him at No. 7 on our list.
Out of all the celebrities in the top 10, Kutcher is perhaps the most devoted site moderator. His postings offer a glimpse into his private life, like a link to a photo album from Kutcher's Fourth of July visit to the White House.
Rock band Linkin Park, which supplied some of the soundtrack for the summer blockbuster sequel "Transformers: Revenge of the Fallen," has the ninth most-fanned page on Facebook.
Band members Chester Bennington, Rob Bourdon, Brad Delson, Phoenix, Joe Hahn and Mike Shinoda have attracted 2,795,247 fans from all over the world.
Fans can use the page to post comments, view photos and videos, and check out the band's touring schedule. The wall also includes updates on Linkin Park's partnerships and albums, and provides links to "behind-the-scenes" videos.
With 2,765,583 fans, Barbados-born pop star Rihanna rounds out the top 10 list.
Neither the singer nor her management appear to post updates on the page, but her millions of fans can use her page to view photos and videos, and keep updated on album releases.
The 21-year-old singer has earned mutliple MTV video awards, Billboard awards and Grammy Award nominations for her chart-topping hits, such as "Umbrella" and "Live Your Life." Recently, she's been the unwitting center of attention because of her relationship with R&B singer Chris Brown, who allegedly abused her.