I misread the OP. I thought it had to be a TV character. If any fictional character will do, there are too many to count for me.
Milo from Phantom Tollbooth, and Alec, his friend that he meets.
Meg from Wrinkle in Time and Calvin and Charles Wallace, too.
Eliza Bennet, Elinor, Anne Eliot go without saying.
Sophy from Georgette Heyer’s novel, The Grand Sophy.
Merlin from the Mary Stewart Arthurian trilogy.
Eowyn from LOTR. (I don’t want to be Aragorn’s “friend”. Heh)
Agatha Heterodyne.
Yorick Brown…I already feel like I have lost my best friend now that that series is over.
Also, Fry. I want to work for Planet Express.
You don’t want to be the best friend of somebody like James Bond or Superman because then all the evil villains will be targeting you in order to get at them. And being as you’re only the best friend, you’ll probably end up dead in order to give your buddy enough motivation to thwart the villain.
Jo March is a great choice.
Kaylee is great, too.
But to be perfectly honest, the fictional person I’ve always felt closest to is Ramona Quimby, Age 8.
Oh, jeez, this is a tough one. So many characters.
I think Professor McGonagall would be cool to hang out with. She might be buttoned up, but she’s incredibly loyal and fair.
I’d like to join *The Princess Bride *gang and A Knight’s Tale gang…they’d be fun to run riot with.
Chandler was my favorite character on Friends. He was witty and funny, and I’d love to go out for a cup of coffee with him.
I could take House in small doses, and I’d let Peter and Nathan from Heroes take turns rubbing suntan lotion on me, as long as I could take off with Hiro when he has to “save the world.”
I’m sure I’ll be back later…
Oh it would have to be Captain Jack Aubrey. Likes a drink, good in a fight and comes with HMS Surprise (The sweetest sailing frigate in the fleet, if a tad small)
Or
Sam Vimes whom also likes (liked) a drink, is good in a fight. But comes with a troll, cross-dressing dwarves and sarcasm.
OTOH, John McClain’s best friend is almost always somewhere safe and sound, out of harm’s way. It’s worth considering.
Hobbes (Calvin’s tiger friend); always ready with a witty quip. And always available to play games and sports with (calvinball!)
I could do without the pouncing, though.
What no votes for Richie Rich/Scrooge McDuck?
Brian
I was going to pick a Cap’n Jack, too. Harkness, in my case. And I’ll stick with platonic, thank you very much. 
So many possibilities…
I’d want to be a close friend and senior aide to President Josiah Bartlet if I didn’t have to deal with Toby Ziegler, whom I found incredibly annoying.
I’d be very happy sitting in 221B Baker Street, chatting with Holmes and Watson about their past adventures, when the next client is shown in by Mrs. Hudson. That’d be great.
If I didn’t have to wear a red shirt, chillin’ with Kirk, Spock and McCoy would be a blast.
Or being a trusted advisor and family friend to King Elessar at the dawn of the Fourth Age.
=Sigh=
Thomas Covenant. What could be more fun than a moody, dangerous, semi-suicidal leper?
Ok, maybe not.
Belgarath or Ingold Inglorian - wizards know how to party.
Holmes, but Watson would annoy me (self depreciation is my gig, two of us would be intolerable).
Bob The Nailer. I’d spot for him any time, and not bitch too much about being called “Pork”. He’s one of those old boys that would die for his friends or family (or dog), but not until he takes a whole damn lot of bad people with him…
I’d be scared to death being anywhere near Jack Aubrey.
Winnie Ther Pooh. What? Piss off, I like Pooh Bear.
Obi Wan or Han Solo.
Nigella (the British cook) - She cracks me up and I think she’d be fun to hang with.
Dave Chappelle - I’d have a ball.
Mos Def - he seems to be so sweet - witty as well.
Just realized that I was supposed to chose fictional characters. duh.
Richard Jury and Melrose Plant from Martha Grimes’ series.
Not a great movie but in Total Recall; Lori played by Sharon Stone who is the agent pretending to be the heroes wife so that the authorities can keep an eye on him is my total dream woman,I’m not talking about her sexyness/beauty aspect but her total pragmitism,cunning adapatability shamelessness and lack of conscience and fast thinking intelligence shown when she is trying to kill Arnie.
For the life of me I cant think of the reason why on a logical level,it just goes right to the heart of me.
My alternative and safer choice is Pterrys Casanunder who would be good loyal company,entertaining,witty and trustworthy.
The Doctor.
I would love to go adventuring around the universe and I am really interested to see how humans evolve over time and to see what we end up being in a couple of trillion years.
I want to be friends with Geoffrey Tennant. I want him to direct me in a show. In fact, I want him in a number of ways, but I would be mostly happy to have him as a director.
I’d go with Dr. Leah Brahms. Smart, sexy, and helps you with your work. What’s not to like? If she gets tiresome, you can just leave the holodeck, heh.
They’re fictional?
That Ford Prefect sure is one hoopy frood I wouldn’t mind spending some time with.