Whatsapp entered a highly competitive market. They've got the highest active users in the SMS market, and over 400M subscribers within 4 years. How they did it?
They've kept it simple, you don't need to fill up sign up forms and remember your user name. Your GSM SIM card is your identity.
Secondly, they tightly focused on SMS market. Didn't go for multi party video conferencing, screen sharing, and other seemingly cool stuff.
I'm talking about my personal experience, in Italy Whatsapp was discovered just few months later than in the USA but I think that the scenario could be the same. Whatsapp started to propose free SMS on the internet when other competitor where not so many and discovering the powerful capabilities of having an app that could let you not spend money on messaging but that you have on the phone (many other services that were already existing were just through website widgets).
Another important difference was to propose you to chat with your existing contacts, that would receive your messages along your phone number and not an ID or an email or new usernames so that they will always know who's there on the other side. And this is a feature also for the user that don't have to remember a new ID and a new password. Whatsapp is, most of all, simple and does just what you need and what you want: he lets you send messages to your friends. Many others apps were used to let you find new people (more like an online meeting service) or there were so many ads or with difficult user interface. Whatsapp is a stable applications, very little bugs and really powerful uptime of their servers.
They also had the patience to don't give up at the first time and just let more users every day discover the real utility of this service. Today Whatsapp is still growing because if you install a new messaging app, at the moment, you will find a little number of contacts already using that specific one and that are all, anyway, on Whatsapp too so, why should I use so many different app when I can use just one? Today Whatsapp has become a verb that so many people use with the meaning of "send a SMS" so it's like when smartphone were starting to grow up that a lot of people used "iPhone" instead of smartphone even for different brands (or like the word "iPod" instead of mp3-reader)
Another interest point is that Whatsapp listened to its users and, step by step, introduced new functions like adding contacts information or sharing position, or even hiding your online status when it was the moment and specially after testing them so they were sure that it would not crash and was actually effective!
Is this question oriented to understand if there are possibilities to develop a new application that sends messages like Whatsapp? If so this is my suggestion: do not try to create a new version of Whatsapp, just think at something completely different that could capture your future user attention and introduce them to a new era of sending messages. If you copy you will just follow, if you create you will be a leader!