Wow, what a tough question.
Given all of the answers here, I can see that I have a lot of experience to gain with gear. And so my choice of 'best' trout reel is limited to the few reels I've owned and fished (LAMSON LITESPEED, SAGE 2450, ROSS EVOLUTION LT, ORVIS BBS, ORVIS BLA, HATCH FINATICS, ORVIS CFO)...
Since we're talking trout (eastern trout for me) most of the reels I've fished are probably more than I need. That said I consider my best reel(s) to be the Hatch Finactic series:
They are built like tanks
The reel is machined from 1 piece of aluminum no screwed on foot (the fewer screws the better)
Completely sealed drag (the less I have to screw with it the better)
Aesthetics is completely subjective but I have to say they look great. I'd love to pickup a limited edition someday
All this aside, if I had to pick the 'best' trout reel based solely on its staying power and influence on reel design, I'd have to go with the CFO vented reel design from 1874 which was revamped by Bogdan in 1974.
I do have a Saracione Mark IV coming in the mail so that might change my answer.