Depends. I usually go first to my American Heritage 4th ed. because it’s out available and accessible on a stand—no need to wrestle a big old heavy tome off a shelf. It’s great for pronunciation and has that wonderful appendix for roots.
For thoroughness and depth, I want the OED, which I have in two condensed (the pages, not the content—need magnifying glass) versions in my living room, along with the Am. Her. 3 and the big Webster’s Third.
For feeling like I really have a book in my hands, I want the massive Webster’s, which takes a different slant from the OED and the Am. Her. When I’m seriously questing after something, I consult them all plus a stray Random House that’s nearby on a shelf. For a subset of the big Webster’s, it’s the handy collegiate, not a serious dictionary by my standards but often cited as the house standard by business clients.
If I just want to get a grip on something quickly, I use Dictionary.com, but I don’t ever stake my reputation on what I find there. It’s just a convenience.
For specialized purposes there are dictionaries of several disciplines, more like little encyclopedias, actually, and a variety of language dictionaries. I also use two children’s dictionaries, which don’t have a lot of breadth but are wonderful for getting right to the essence of the terms they do define.
I guess overall the OED would be my favorite (it’s the one I’d choose to keep if I could have only one), but I turn to the Am. Her. 4 most often.