This is one of those questions that doesn't have a cut and dried answer. Everyone will give you a different angle... and tell you that the next guy's full of it. That being said: here's my answer...
I know <U>how</U> to tie probably 3-4 times the amount of knots I actually USE. My personal top5 are
Uni knot- for making a loop in my leader, making a line to line/leader connection, attaching line to spool
3-turn improved clinch not- for attaching hooks to leader (this will be a thorn to most, but it's always worked for me)
Albright Knot- for attaching heavy leader (mono or coated seven strand) to line/power pro
Bimini twist- best knot (IMO) for creating a double line
Spider Hitch- fastest knot for creating a double line
Figure 8 Knot- for attaching coated seven strand to hooks/jigs
These are the knots that I tie most, and that I can tie in the heat of battle, FAST. Of all of them the Uni is the most versatile and quick. Definitelythe one that I would key in on learning, and learning to tie properly. From there learn as many or as few different knots as you want, but I think you'll find you'll still tie the Uni-Knot most often.