Prepare for my infamous walls of text.
The fact that you are playing a character who is filling in a role no one else can do doesn't mean you can't have fun with the character, or that he won't be interesting.
So, basically, what you need to do is to think on multiple levels. Let me simplify my answer with some of my own experience.
I love rogues.
Oh, no, I don't think you understand.
Every manifestation of them. Pickpockets, cat burglars, assassins, acrobats, spies, swashbucklers, you name it. Once, in Pathfinder, I had to play a tank, as no one else could fill in the role.
I forgot the fact that I loved rogues for a while.
I imagined the game as if it was a movie. A movie that I had watched, but forgot. This is a very important step to keep in mind for the rest of my answer.
So I sat down and tried to remember who my character was. The fact that he was a protagonist in a movie meant that he must've been interesting. But he must also have had some characteristic, or more, that distinguished him from similar roles in other movies.
So I gave him some unique characteristics. A crimson red full plate armor, no weapons (I made him a pacifist) a mirror tower shield (so that his enemies could see their faces as they slowly realised they couldn't harm this guy :P), white hair, even if he looked in his mid 30's, and an eyepatch.
These things look good, and they help me remember the character, but what makes him interesting? Why did I like him when I saw him in that movie?
So I gave him a story for every one of his distinguishing features. The eyepatch, the white hair, the armor, the massive mirror shield and the fact that he did not use weapons.
Ok, so now I remember why I thought he was interesting. But what gives me the hint that he was in that particular movie?
How does the character fit in the world? How does he treat others, what are his worldviews, his ethics and ideals? Why is he doing what he's doing, where is he from and why is he here?
And suddenly, I remember it all, and it makes sense.
So, to summarise:
- Create an interesting appearance (doing this will help you develop your character's backstory - Why does he have/How did he get those features/equipment/speech patterns/sayings/scars?)
- Create an interesting story and background for the appearance(doing this will help you develop your character's personality - How did acquiring those features affect him? Did he have them since birth, or did they develop? Are they part of his religion, customs of his homeland, rank or did he choose to have them for personal reasons?)
- Create interesting reactions your character had to his background; in other words, give him personality (doing this wil help you develop your character's motive - Why is he doing what he's doing? How does he view the world? What has his background made him best at? For example, this is where you would put adjectives to your character, i.e. sneaky, honour-bound, loyal, friendly, chatty, bitter, etc.)
Follow these guidelines, and any role you are called upon to fill, you will do so in an interesting and memorable manner.
Hope I helped. :)