Saw this somewhere (am I allowed to say where?) and thought it might be a fun thing to find out.
How about this: It has to be a singular (no teams, no alien races as a whole, no duos) science (has to have a clearly intrinsic and fantastical science element) fiction (has to have a clear author and starting publication date) character (no plot devices, must be a comprehensible individual).
Examples of no-nos would be: no collective crews of the starship Enterprise, no Daleks as a whole, no Mulder AND Scully as one entry, no Batman, no Wonder Woman, no Lord of the Rings characters, no Game of Thrones characters, no religious/mythological/historical figures, no Monolith from 2001.
Example of allowables: space opera, space fantasy
Remember, this would be The greatest, not Your favorite. Greatest here would include both historical scope of influence (real people and other fictional characters they've since influenced), contemporary value (how much more they would be valued over other individual fictional characters today), depth and variety of stories starring said sci-fi character available, versatility of interpretation of said sci-fi character, continuing success in different media, instant recognition, etc.
Let's score it up like this:
1. First Place (20 points)
2. Second Place (10 points)
3. Third Place (5 points)
I'll go first and keep a running tally for as long as anyone is interested.
1. Clark Kent / Kal-El of SUPERMAN (+20)
2. The Doctor of DOCTOR WHO (+10)
3. Spock of STAR TREK (+5)
Please list The Three Greatest Science-Fiction Characters According To You!