I've tried other browsers and I keep coming back to Dolphin because it has some things that nothing else has that I've found. (This is on ICS)
* Gesture-based commands. I read a lot of long text pages (OK, very long text pages), and I love that I can tap in the bottom left corner and swipe a V to go straight to the bottom. The reverse gesture also works, and there are both forward and back options as well, though I don't recall which gestures I've added and which were already there. I may have added the "Close current tab" one. By the way, you can also define your own gestures. I think this may actually be my killer feature for it.
* Tabbed browsing that works well for me - I can long-hold on a link and "Open in Background" then go to that link later, though I'll admit that this sometimes seems flaky - I've had enough times where it failed to open the link that I sometimes verify with a quick downward swipe on the page to make the tabs show at the top.
* Plugins - in particular, quick access to LastPass and Save to Pocket - I have others but don't tend to use them. these are accessed by a swipe from right to left.
* Bookmarking and bookmark editing - A swipe from left to right will open the bookmarks, nested folders are available, hitting the gear icon lets you edit, etc. There's some sort of synchronization available, but I don't use it.
* Simple home screen customization - I really have 4-5 sites I hit most often, and they're right there with one click when I start the app up.
* Various useful menus for tab operations (long-hold on a tab) and page operations (long-hold on the URL field).
* Dolphin Jetpack - I can't overstate this one enough. For a long time it wasn't clear to me which browsers were actually doing their own rendering vs. being a skin on the built-in Webkit. With Jetpack, Dolphin has its own much-more-updated rendering backend with HTML5 support, etc. and for many of the pages I read the performance difference is extremely visible.
And addressing things that other people have commented on:
* Full-screen mode is available with that same right-to-left swipe.
* There is a privacy mode but it's inconvenient (Menu-More-Settings-Privacy&Personal Data-Private Mode). You can create a new gesture to switch quickly to "Browsing without history" but I'm not sure if that's entirely the same thing.
Biggest annoyance:
* Using Swype beta and entering URLs, the combination of Swype attempting to do autocompletion and Dolphin trying to do autocompletion is painful at best, and I've had occasions where Dolphin will just silently die (e.g. trying to type in "baen.com/Eleutherios.asp" which died after I'd been poking around writing this, but worked fine after I restarted Dolphin).