Yes, it will depend on which country you're traveling to and the agreement between your country and the destination country.
Anyway, as for those coming to India according to incredibleindia.org (India's Ministry of Tourism website) - it's mentioned there that Tourist Visa has a Period of 6 months.
The site was not very clear what it meant by PERIOD, though. (OR, it's just me who's confused - and it means multiple entry within the validity period of 6 months.
Anyway, the site also mentions the following:
Nepal/Bhutan - don't need visa
Maldives - don't need visa up to 90 days
Citizens of Finland, Luxembourg, Singapore, New Zealand, Japan, Cambodia, Laos, Vietnam, Philippines, Indonesia and Myanmar - are granted a single-entry Visa on Arrival for a period of 30 days.