Passport
You must carry your passport with you at ALL times. This is a requirement by Indian Law. Failing to do so can land you in jail, or you may have a hard time at the police station. Not carrying your passport can also end up in heavy fines.

Your passport must have atleast a 6 month validity period in order to enter India. If your passport is expiring before 6 months from your date of entry into India, you may be required to leave the country. In extreme cases, you may not be allowed to enter India if your passport does not have a minimum of 6 months validity.

Visa
Same rules as the passport. Visas can be extended in New Delhi at the MHA (Ministry of External Affairs) office. Prepare to wait in line for days. You may have to visit the office for 5 - 7 days before you get an extension. It is always best to get a five year multiple entry visa for India if you plan to stay there longer than 6 months.

If you plan to stay in India for over 180 days, you must register with the FRRO (Foreigners Registration office) within the first 3 days of your arrival in India. This is a free service. If you do not register within the first 3 days, you will end up paying US$30 per person for the registration process. Over that, it is not gauranteed that you will be given an extension to stay in India for over 180 days.