Since there is a lot of them I figure a poll would be a bit too big and limiting to one tool.
Lets get this rolling with my favorites.
Basic manipulations move rotate scale
Extrude, Merge, Turn Edge, Smooth Vertex, and Loop Cut and Slide.
I Like All Of Them =) lol
THE most? Why, select off course!
Also W-key Subdivide & then tweak them resulting points according to need,
either via edge slide, grab, rotate or scale(for this last two I usually use the active element as pivot).
Mirror & SubD modifiers always go hand-in-hand.
But all in all, I use any feature as long as it has the particular effect I’m going for the fastest.
Workflow:
Extrude, select, Make face.
Edge Slide, LoopCut, Make Face and Extrude are the ones i use the most. And of course, Remove Doubles.
extrude, edge slide, loopcut, bevel, bridge, knife, tris to quads, merge, remove doubles
Extrude, knife, bevel, inset, rip, bridge.
Loopcut, extrude, (fake)knife, remove doubles, inset, makeface, bevel, bridge.
In that order.
Nice, I honestly wasn’t expecting such a number of responses already!
@Freemind hmm, let me guess point by point modeler? 
I am mostly an organic modeler, and yes, mostly point by point 
I’m allways trying to ahieve the geometry with the least polycount possible, and I feel in control when doing so.
But I do get into other methods…
Inset outline, fillet, multiple fillet, looptools, loopcut, bevel, edgeslide,vertexslide…
Im very satisfied nowadays…
the usual suspect that just about everyone has mentioned, but ones I use a lot are
CTRL+RMB point extrusion, vertex snap with Automerge Editing…loop cutting but I am missing all the finer controls from 2.49 (S,P,F)
@Tungee, not sure which version you’re currently using but you might be happy to know that BMesh combines Fillet with Bevels.