Most of the long distance trains in India have bookings opened 90 days before the train ride. There are some that have a shorter period available.
Which exact Indian trains have reservations open only 30 day prior to departure?
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Indian long-distance trains open for bookings 90 days before departure. Some shorter-distance inter-city trains open less than 90 days ahead, for example Delhi-Kalka & Kalka-Simla generally open 30 days ahead.
There may not be a hard rule which trains fall into the 90 or 30 day category. If you are interested in a particular train, you can try to book it online 60 days in the future and see whether you can book it. You can try cleartrip or the official Indian railway site
Interestingly enough cleartrip allows me to book 'Delhi to Kalka' in April 2012 (88 days from now), so the 30 days mentioned above may no longer be correct.
According to the Indian Railways site
Advance reservations are made generally up to 90 days in advance for all classes and all trains. The period of advance reservation (ARP) is exclusive of the day of departure of the train.
At intermediate stations where the train arrives on the following day, such reservations can be done 91 days in advance of date of journey from the intermediate station. ARP is in relation to the date of journey from train originating station. In case of some Inter-city day trains, the ARP is less.
You can get a partial list (though not official) of Inter city trains from Wiki