Harvey Dry Fly Knot
The Harvey Dry Fly Knot, developed by legendary fly fishing instructor George Harvey, is probably one of the best choices for connecting flies with up or down-turned hook eyes to your tippet. It's a strong knot and it lets you avoid passing an open loop over a bulky fly pattern during the knot-tying process.
 
Insert the tag end through the hook eye and bring it back toward the standing line.
While holding the standing and tag ends just in front of the fly, make a small loop around the standing line, then make another of the same size and hold the two loops together.
Push the tag end through the loops and make two wraps around them.

Hold the bend of the hook in one hand and pull on the standing line with the other to cinch the knot. If you've done it right, the two loops will slide back and pop over the hook eye, leaving a straight connection between line and fly. Trim the tag end.