Without Linux there would be no Android and Apple would by now own 95% of the smartphone market(1). Server infrastructure across the industry, including Web hosting, would cost an arm and a leg due to proprietary Unix license costs. Services like Rackspace and AWS would likely be barely viable, if at all. A generation of geeks would have grown up probably on Windows without Linux to cut their technical teeth on.
Linux success is a bit like that of SQLite. There are probably over 50 SQLite databases in the room with me right now, on the smartphones the other people here have in their pockets, but you'd never know it. It doesn't matter if anyone knows it or not, in fact the technology being invisible is the point. It's why even the fact that OSX and iOS are unix under the hood is such a triumph.
The goal might have been Linux on the Desktop for some, as a back end guy for me that's always been a distraction. Mobile is making the Desktop almost irrelevant, or at least a niche market, and Linux and Unix are right there, out in the lead. They run the client devices in people's hands, and most of the back end services those devices rely on. They own the future.
(1) I'm a happy loyal iPhone user, but I'm not stupid enough to not realize that would be a bad thing.