There are probably more browsers than you are aware of 1 2.
This is the second public version of this article (and my first two copies never went public). The first is html5-market. As I wrote last time, the browsers that you think are important is dependant on what your target audience is. Read 3 for more perspective on this. There is a luxury hotel chain, whose biggest browser is ipad safari, so they have to do alot of optimisation for that specific situation [reference: lecture by that hotel chains CTO]. There are many browser stats written by tech companies, with a mostly tech audience, who report different values to normal users. I think writing websites limited to tech people is fairly silly, unless you are selling a product that only tech users will buy heavily.
Depending on who you talk to, use of internet exclusively by mobiles is really common [XXX] [XXX], or suggested (the type of b2b products that I build currently are too dull for our clients to use them out of hours in any fashion). Tech audience generally have higher investment in devices, and much higher usage; so are unlikely to browse purely through a single device.

Important webrowsers for “casual internet”

I am using Wiki, BBC and ebay as examples of “casual internet use”. These will have broad spectrum users, with a wide variety of technology. Please note, as a working document for work; these are sites based towards UK audience. My clients/ employers are UK based, their clients are mostly UK based (or UK branch of client).
Wiki used to report browser usage e.g. 4, but they have stopped collating this data.