As some have pointed out, unless you live in a remote area with little competition or not enough clientele in one genre to support a business, like in Alaska, yes, you need to specialize. This is especially the case if you intend on doing any commercial photography. Why?
In reality, people are hiring photographers today for their vision. It is nearly impossible to develop a vision that can be applied to all genres; different genres demand different shooting techniques. Therefore, if you try to shoot everything, you will spread yourself too thin and never really develop a vision that is distinct. Even if you happen to develop one in a particular genre, if you continue to work in all genres, you will likely confuse people and they will not notice it.
Furthermore, if you intend on working with advertising agencies and PR firms, you will not be taken seriously if you shoot weddings and events also, or at least show that on the same website. This may not be fair, but it is how the business works. Don't try and come up with clever arguments on why I may be wrong or how you could manage it; it won't work. You will be known as the guy who shoots weddings, so far as art directors are concerned, and just be ignored.
Last, even if you don't care about having a style and still want to shoot everything, it just won't work. If you don't have a style and a particular speciality, you are pretty much going after the work that does not need one, the projects where the ADs need a handful of generic images. You may think there are a decent amount of projects that fit this description, but with so many inexpensive stock agencies that provide a large selection of images for an AD to review today, in real time, they are nearly non-existent anymore. It is easier, cheaper and faster (which is cheaper) for ADs just to find the images they need at [pick any one of the dozens of stock sites] then ... to search for three photographers, bid out the project, set it up, have it shot, retouched, etc.
My advice, pick a genre you are truly interested in (I shoot still life and architecture, which is still life at a greater scale), look at others work, and shoot and shoot and shoot. Pound the pavement, get gigs, put your all into them regardless of how crazy or disinteresting they may be. In five years you'll have a style and then you'll start to get noticed by the better clients.