Developer: Opera Software
I use my palmtop quite extensively for web access these days, at Uni I have access to a very good coverage, free Wi-Fi network which means I can check my mail and browse forums etc. while sitting in a coffee shop on campus etc. The built in browser on my palmtop (Palm Tungsten E2) is Blazer. Although functional, this browser really doesn't seem to perform that well to say it has nearly a monopoly on the platform as far as I can see. However popularity doesn't necessarily mean much (look at IE!).
Among the faults of Blazer, are it's inability to display some pages in a legible fashion, notably the BUNCS forums that I visit regularly, I have become used to it's display and can use it, but it's not good. Also it is incredibly slow at doing anything. Opera Mini however seems much more efficient at loading pages, and can often come up with a better render of them on a small screen.
However, the operation of the Opera Mini browser is far from smooth, I have experienced multiple crashes and apparently at random, however I am running it on an officially unsupported hand held. For anyone interested, to get it working on my palmtop (the Tungsten E2 as I said before) I got the IBM Java environment required from Palm, it's a free download for Tungsten E2 owners. Then, I installed the generic version of the software (from the Opera website) using the built in install function on the Java client.
Some nice features of the browser that make up for the lack of support and frequent crashes, are the tidy and simple bookmarking system, making accessing the web easy, and the feed-reader, a handy little RSS feed reader built in to the browser that can allow you to use live bookmarks even on a palmtop, a function not seen in Blazer.
I am waiting for the Opera Mobile browser to be ported to the Palm Tungsten E2, since this is a much more usable browser, however, for fast access to the web from a Palm hand held, Opera Mini is probably worth putting up with for now.