- [Android]Firefox mobile: Even before the native app version was released, this was my favourite browser for a nuber of reasons. The UI is easy to use, it's technically accomplished - as good as the desktop version, it's updated regularly, there is a good catalogue of add-ons (including Adblock) and the sync between devices and desktop just makes life that little bit easier. Especailly now the native version is available, if you're on Android then you need a very good reason not to be using Firefox.
- [Android]Opera mobile: This is the only other desktop equivalent browser and is every bit as accomplished as Firefox in terms of browsing experience but I don't get on quite as well with the UI. Opera sync is pretty good especially if you're also using Opera Mini.
- [iOS]Dolphin: This uses the stock browser rendering engine and is mainly a UI wrapper that is a really big improvement. The big feature of Dolphin is the ability to use a 'desktop' user agent to get round sites that do a bad job of mobile detection. In terms of UI improvements, if you're using an iPhone then the browser chrome (address bar at the top and menu bar at the bottom) takes up a large portion of a screen that isn't particularly big to start with, Dolphin not only removes this but also has a full screen toggle that does exactly what it says on the tin. You also get tabs. For people with a mix of Android and iOS devices (Anecdotally I've noticed that Android phone and iPad is an increasingly common ownership pattern) then Dolphin sync will keep both devices in sync which makes switching devices throughout the day a much more pleasant experience.
- [iOS]Safari: The stock browser on iOS 5 is still lagging behind the top mobile and desktop browsers but it's better than the stock browser on Android. The UI isn't the best and I can't see any reason to use this over Dolphin.
- [Android]Dolphin: Pretty much everything said for Dolphin on iOS applies here too. If your Android phone can run Firefox then you probably should use that. If it can't, or you want to sync with an iOS device, then there no reason I can see to use the stock browser over Dolphin.
- [Android]Browser: The stock Android browser is pretty poor. It's better in Honeycomb and I've not tried Ice Cream Sandwich but my advice is to steer clear as much as possible.
- [Android] [iOS]Opera Mini: As it does everything on a server-side proxy, this is the only browser that is available on both Android and iOS. I've put it last because it's not really suitable for everyday browsing but where it absolutely blows the other browsers out of the water is on a slow connection as it transmits an absolute minimum of data. If you've got a poor signal or are incurring roaming data charges then Opera Mini should be your first choice of browser, just don't try and use it for dynamic websites.
There are a number of less popular browsers missing from this list in the name of brevity but the big omission is Chrome on Android. Unfortunately I don't have an ICS device at my disposal so haven't had a chance to really use it.