What to Bring
Don't bring too much.
There is a perception of India as lacking in creature comforts and material goods. Not true. A traveler could easily arrive in India with nothing more than the clothes they're wearing, a passport, and some cash. Everything else can be purchased here. The price, if not always the quality, would be better than they'd pay at home. And many purchases made here would be more appropriate for local conditions. The message - don't bring too much. Travel light.
Buy Things Here
Not only does it help the economy, but also you'll usually save money. Buying much of your gear locally helps ensure you're well suited to the culture and climate. This is particularly true of clothes, which make up the bulk of most travellers' baggage. The clothing most Westerners perceive as appropriate casual wear for a hot climate may be extremely inappropriate here. Westerners deal with heat by wearing skimpier clothing. This is not the best way to deal with the heat and blazing sun. Indians opt for more flowing garments in cool cottons and you will realize why. (Please see the fashion section of "Culture Clashes " for some suggestions here) Either you'll wear those summery clothes you bought and get unnecessary hassles and sunburns or you'll carry them around while you wear something more suitable.
Leave your sleeping bag at home
Unless you plan extensive trekking in the mountains, a sleeping bag may prove cumbersome. Especially in South India, where the climate is fairly warm even in the winter months, a locally bought, hand woven bed spread is much better for use on the train or in a budget hotel than a fancy sleeping bag, and much more versatile. It can be tossed around the shoulders like a shawl if its chilly, folded into a cushion on a long train ride, used as a towel in a pinch, and function as a beach mat at the ocean. It will look great back home, too.
Shop in big cities
Not everything is available everywhere, of course. Many products cater only to the urban middle class and will be most easily found in the larger centres. Keep that in mind if you are heading off to a rural setting for a few months. However, most travelers pass through the bigger cities regularly and shouldn't have many problems.
What you might need
Here is a listing of some of the things that are still difficult to find here.
Swiss Army knife - Useful for all manner of emergencies, from opening beer to repairing shoes.
Small flashlight - Can be bought here, but a little Maglite is a joy.
Towels - The ones here don't seem to be very absorbent. Bring a small towel. It will usually dry fast.
Cotton socks - They seem to sell thin nylon socks here. Good cotton socks would be more appropriate.
A good, small lock - These are available in India, but a foreign one will be much harder to pick, if anyone is so inclined.
Women's swim wear - Available here, but most of it would please your grandmother more than you.
Cameras and computer gear - Latest models are not available, and prices may be higher.
What you won't need to bring
You can buy most types of toiletries in India. Soap, tooth paste, shampoo, tooth brushes, disposable razors, shave creams, even contact lens solutions and cotton swabs. Besides a range of international brands selling everything, you'll have a chance to try Ayurvedic shampoo preparations, soaps made with sandal wood oil, toothpaste with neem, and other exotic toiletries you won't see at home. Tampons (only Regular size, though), condoms, and sanitary pads (but not Mini pads), as well as most over the counter medical preparations and any prescription drug you'd care to name are available. Do not bring a large medical kit. Drug prices in India are very cheap and the quality is good. Unless you have a specific medicine you need to take regularly, buy your kit here.
Contact lenses, eyeglasses, even good quality dental work are available in India at a fraction of the cost of that in Western countries. So are watches, clocks, flashlights, and leather goods. So are most batteries, including common watch and camera types, though less common camera battery types may be difficult. Film and film processing is readily available. You'll get the best quality processing at the larger film labs in big cities, but many small outlets do acceptable work.
There are bags, wallets, and garments of all types: jeans, T-shirts, dresses and suits, as well as traditional Indian fashions. India exports large amounts of these goods to the rest of the world. Major cities have streets selling fair quality " seconds " for ridiculously low prices. (Just remember they are seconds and will have at least some minor flaw.) Major international clothing brands also sell their products in up-scale stores.
There are a great variety of shoes made in India with a range of styles and quality. The selection will be best in the larger centres, as will the range of sizes. However, large sizes are hard to find. American men's size 10-11 is the common upper limit.