Think Internet Explorer. Still significantly more popular then other web browsers. Lets put aside its ifamous incompatibility with w3c standards and concentrate on its security. Or insecurity rather. A friend of mine got almost scammed lately by an online banking password harvesting trojan. Happened under IE and wouldn't happen under say Firefox or Opera... at least by now.

Unfortunately it's not very likely it has something to do with a more secure design or a better coding of the alternative browsers. The design of each browser gives a choice of virtually the same amount of potentially vulnerable places. Also the code is similarly big and complicated and thus bug prone. What is the difference then?

It seams like nothing more and nothing less, but the popularity.

Even if you had a perfectly exploitable flaw in say Firefox, it's times more profitable to find and exploit one in a lot more popular IE. So, just wait until the alternative web browsers gain more userbase and it's pretty likely we'll see the amount of attacks on them comparable to those aimed at IE.

The bottomline — the more popular something is, the more impact on security it can potentially have.