The head shake and the first jolt when you set the hook. I hate the one where they take off again when they are at your feet. I lost a monster at Oak Orchard once after about 20 minutes. The hook just pulled out. The fish swam back over and laid in front of me. If I would have had my pistol, I would have shot him.

For me it's gotta be the take and the initial run. Hearing that drag scream and wondering if it's going to take me into the lake.That really gets my heart pounding.

The anticipation.............................the take...........the set......next !

SUNF - Great question.  For Steelies has to be when the indicator stops, the lift (hookset), the heavy thumping/headshake which turns into that first run.  Hookset for sure.  The thrill I did something right that made that fish take my offering. 

Muskies - OH MAN! the screaming reel trolling or that "I just hit a stump with my Wiley jerk...crap thats a fish dummy set the hook" feeling (which all takes milli-seconds).

Yeah, I've had bank jumpers. Best one ever though, as soon as I hooked it, ran directly at me, jumped and hit directly on my chest. 
 
 
My buddy had a "bank Jumper" at the elk access, unfortunately it did a header into the rocks, shortest battle I've ever seen, 2 seconds after he hooked it, the fish was out cold.

My favorite part of fishing for steel is the initial hookset, when the float goes under.  Too often the float goes under when the fly gets caught up or the shot hits a stick or something, but when that float goes under and you snap back on the rod and feel the weight of the fish and see that initial flash in the water, that's what keeps me coming back.  I especially love it when the water is that deep shade of green and the float goes under and the fish flashes, but you clearly couldn't see the fish sitting there. 
 
Some of the aerial shows I've had in the creeks are a good time too, like the fish that jumps over one log and then heads under the next one.... 

The Strike! Nothing like a steelhead cracking a streamer at the end of a drift

The run and leap airborn.

The hookset and initial headshake really gets me going.  Second is the picture and release.  This is the part that I have the most fun with when I'm done fishing.  I can go home, upload, edit, and share pictures of my day.

After catching some whoppers casting spoons into the lake last weekend, I may have to renig onthe initial dunking of the float.  Thanks for the responses everyone...ALL excellent, I might add.

i'd have to go head and say my favorite parts are the initial strike and then that second run right when you almost have it banked... she isn't done yet