I have seen, people do start telling much of a detailed story in an interview. If you have gone for a technical position, then you should limit yourself to 3 major terms: 1) education 2) experience 3) skills for which you are there.

For a technical position, why start like this: “I ABC, 30years old, belongs from XYZ city of PQR state. I got married in year XXXX and have 2 kids. I did my graduation from MNR in computers and masters from RST. Then I joined a small company CMP in XXXX, and since then I am working….”

Interviewer is there to find a suitable candidate for the position and not to listen the detailed stories. They have a very limited time and a great challenge to judge a candidate and select the suitable one from so many applicants. So, be specific and to the point, while answering.

Note :

In marketing or traveling oriented jobs, interviewers wish to know about your personal details. It matters, because this job profile requires any time traveling and city movement.
But, in technical profiles, relocation or office transfer is not much and is limited. So, you don't need to waste any time in speaking about your personal details, rather talk about your professional expertise and experiences.

A legend, Shivprasad Koirala sir, also, suggests to be specific and speak about the relevant details only.

You can go about your answer like: "I have done my graduation in this, and masters in this. In terms of experience, I have so much experience particularly in this n domain. Currently I am working with this organization on this project and am using this n this technology..."

After saying this much, pause and notice the reaction of the interviewer. He may be OK with this much brief of yours. If the interviewer is OK with this much answer, he may then ask you like this “OK, Can you brief me about your current project and your role?”.
I would like to highly recommend you to not tell interviewer that where you want to see yourself in the next 2-3 years unless and until you are asked about this. I feel, Indian interviewers are not mature enough to hear this from you with "tell me something about you" :( . So, if asked, only then tell about your prospective position in coming time.
Your experience & feedback is welcome.