Here is a chart of the last six years of relatively believable browser share #s (from Net Applications via Wikipedia). In it you can clearly see multiple alternative browsers gain a foothold in the market.
Anecdotally this seems true as well. I know plenty of people who use each of these as their primary browsers, with the exception of Netscape (not sure what is going on there--AOL?). And more often than not, it seems people actually switched to these alternative browsers (as opposed to being forced on them by their OS, OEM, IT dept, etc.).
Is this an apt analogy for the future of the search engine market?
I'm hesitant to quote any search engine share market #s currently because I frankly just don't believe them, or at least they don't seem to line up with anecdotal evidence at all. Google seems currently way more dominant than they sometimes get credit for.
Yet at the same time alternatives are arising. And more importantly wrt to the analogy, there are alternatives that in my opinion offer a different enough overall search experience to be preferable to some people, much like Web browsers.