This is a question that is kind of vague. If it’s talking about pre-defined characters such as Drizzt or Bigby or Tanis Half-Elven or whatever, I don’t really consider them PCs. Even when I was involved in groups running the original Dragonlance modules, I didn’t really consider them PCs. They were NPCs that we’d temporarily stepped into playing.
I’ll interpret it, rather, as the favorite type of PC that I like to create and run. First, I like to have some sort of tie in to a previous PC or NPC. It’s never something big or something that really affects the gameplay aspect of the character. I just like to believe that all the great “heroes” have some thread that ties them all together. For example: my good then evil then neutral-ish mage Endeleban Losteast and my one-armed paladin of Helm, Terun Eastmore, are actually brothers. They are the middle two out of four sons of a Purple Dragon general. Delban was disowned for not following in the footsteps of his three brothers and joining the Dragons. He always preferred arcane studies to that of a warrior. Terun eventually found his way into the order of Helm through other events.
They are the two most closely related characters I’ve played. Others include two clerics of Pelor who both came from the same sanctuary. One took up the same quest as the other after the first one vanished without a trace. Another was a dwarven ranger who served an NPC king the group encountered in another module. And so on. Probably 80% of my characters have had at least some thread that tied them to a previous character or NPC from the Wyrmfang Chronicles.
Second, I like my characters to have a flaw of some sort. Whether it’s a paladin whose ideas on being a paladin aren’t quite the standard point of view, an elf who hates all other elves, or a character appointed as party treasurer who’s stealing funds from said party treasury, I like that there’s something that isn’t necessarily “heroic” about them. The last one was mildly amusing because we ran through pretty much the entire campaign arc without anyone figuring out that he was skimming about 10% off of the party treasure for himself. I don’t think they’ll ever ask me to be party treasurer again.
Third, I like for my character to be driven by some overreaching goal that happens to align with the party. He needs to have a reason to align himself with these people he normally wouldn’t. I’m not a fan of the “You look trustworthy!” approach (bonus points if you know the reference). Whether it’s a bard looking to restore his family fortune, a cleric seeking a cure for a mysterious plague or a mage lusting after power as a shortcut to greatness. My current character is a cleric of the old Osirion god Ra who is seeking to draw the old gods (read: true gods) back to Golarion by restoring worship of Ra to the Pathfinder world. He believes doing so is the only way to restore the true line of pharaohs (read: overthrow these ridiculous pretenders and restore the seat to the proper family) to the land.
Aside from those three points, I typically like to throw a lot of variety in there. Some people like every character to be the same: elven wizard, human barbarian, dwarven ranger, whatever. That’s fine for them but I don’t care for that. For me, playing the same character over and over gets old fast.