Twitter is not new to anybody and its a free service. Good news is that it will be free as per Twitter Co-founder, Biz Stone, it will be soon coming up with some programs to make money and sustain the growth.
I feel, the growth of twitter was for many reasons like a free tool to communicate, device updates, API feature. Its very important to generate money to keep any company running. Twitter was funded by Venture-capital who usually fund such kind of projects. Twitter is very successful as on today, but the existence depends on how they go in future. Recent DDOS attacks has triggered them to think about a system to avoid such future threats.
A common twitter user, who tweets for fun will never go for any subscription. People who make money from twitter will be targeted by Twitter. I feel twitter is a good marketing tool reaching a good crowd. The future and existence of twitter will purely depend on their revenue program / subscriptions