On February 25, I finally received my Offer of Admission! I received an e-mail informing the school's decision had been released and I should log into my online application to check it out. It seems the e-mail is the same either you've been accepted or not, so receiving an e-mail by itself does not mean it's bad news or good news.
After logging into my application, I found a letter and a form to tell they if I accepted the offer or not. The letter is from the Director of Doctoral Programs and it included congratulations, my student ID, details about the financial aid package which is part of the offer, and the information that I have until April 15th to accept or decline the offer.
After waiting for such an excrutiating period, it takes some restraint to not accept the offer immediately. But the right thing to do is to wait until you are certain about your decision. There is a lot of debate about the possibility of accepting an offer and declining it later if another better offer comes up. But, in my opinion, just don't do it. Even if it is possible (and that's a big "if"), it's not considered ethical by many people in academia, and it's not a smart thing to do since you're not forced to decide early. Once you accept an offer, it should be your final decision and you are giving up all other offers.
Since I got my offer on February 25th and the deadline to accept the offer is April 15th, there is a long time. If you have time, use time wisely. First, I suggest doing even more research about the school, talk again with professors, friends, relatives, to get other points of view. Second, if the professor who interviewed you was open to it, get in contact to thank and maybe take the opportunity to ask further questions you probably have now that you've been accepted. Third, get in contact with the other schools you applied to, to inform them you have received an offer and so you would like to know if they have any news for you. If you are asking it so early, like me, most schools will answer they are still reviewing applications and you should wait. But a few of them were able to provide unofficial answers. One school did not answer it directly, but said that I should take the offer I had, for example.
So you can reduce the list of schools you are waiting for. By the middle of March, you probably will have a decision from most schools you applied to, but still nothing from some of them. I accepted my offer on March 15th. It was early, since I still had a month left until the April 15th deadline. But then, I had received rejections from many schools. And, among the schools which had not released a decision yet, there wasn't one that would be a clear winner compared to the offer I had. A couple of weeks had gone since I got the offer and it still seemed like one of the greatest opportunities I could ever find. So, I felt it didn't make any sense delaying things further. But I'm an exception, for many applicants, beginning of April is still a time to be weighting options.