While Callaway golf clubs are undeniably well-made, perhaps the biggest reason for their success is the name they chose for what became their most popular club: the Big Bertha driver. Millions of "Berthas" were sold and Callaway became the big name in "woods". They also created the market for outrageously expensive (at least for the time) drivers. It's both a testament their club's quality and the company's marketing efforts that they've been able to sell single golf clubs for $300+ for many years. Eventually their full club sets gained equal status and the rest is history. You can't watch a golf tournament on television without seeing ads for their products.
And the Big Bertha was only the beginning, as Callaway continued to offer new, "improved" clubs almost annually. One of their latest offerings is the "FT-i" driver, a very different looking club that is getting rave reviews from golfers of all ability levels.
Callaway has benefited from being associated with an excellent group of touring pros (and vice versa, they would insist), such as Phil Mickelson, Annika Sorenstam, Ernie Els, Morgan Pressel, and Charles Howell. And a couple of guys named Arnold Palmer and Johnny Miller. Alice Cooper, too.