The short answer: yes.
Visas obtained in advance of travel are required for all foreign visitors to India, regardless of country of origin, purpose of visit, or length of stay.
International travelers who arrive in India without a passport or visa may be immediately deported. Check the website of your nearest Indian embassy for the latest information, as immigration and customs rules often change.
Tourists who wish to travel to India solely for personal (rather than business) travel, and who plan to stay no longer than 30 days, can easily apply for an e-visa online. The application for an Indian e-visa requires travelers to upload a photo and passport scan, and to pay the application fee, which can vary wildly depending on the country of origin. U.S.-based travelers will need to submit $75, while some countries and territories (Argentina, for example) will have a $0 fee.
If approved, tourists will receive their e-visas via e-mail. They must be printed out and presented upon arrival at the airport. E-visas take at least three working days to process, and should be procured no less than four business days before arriving in India. E-visa travelers are also expected to already have their return ticket, or a ticket to a subsequent destination, upon their arrival in India, as well as sufficient funds for their stay in India. E-visas are available to citizens of 160 countries.
For travelers whose visits are not included within the parameters of the e-visa, applications may be submitted in person to the nearest consulate or embassy. A tourist visa procured in this manner generally allows up to six months of legal travel within India. Extensions are rarely granted.
The U.S. Embassy and Consulates General in India urges travelers from the United States to ensure they have their proper documentation in order, as they cannot provide assistance to travelers who arrive without such documents. The U.S. Department of State also recommends that travelers make photocopies of the bio-date page of their U.S. passport, as well as the relevant pages containing their Indian visa and immigration stamps.