That should be 2+ week trip to India.

I am assuming you don't have an "unlocked" US mobile phone which would allow you to simply buy a local Indian SIM card and use your own mobile phone. If not, then my first suggestion is that you simply buy an unlocked phone now in the US. You can buy them as far as I know (I don't live in the US); or perhaps a friend or colleague has one you can borrow. You can also rent one through Cellularabroad see http://www.cellularabroad.com/ or possibly your current service provider. This would save you the time and trouble of having to do this in India; although it probably is a bit more expensive than renting or buying in India.

Alternatively, if you want to wait until you get to India to get a phone, while I am sure you could rent a phone, my suggestion would be that you buy one. It can't cost much more than renting and you will get a new phone. Plus if you are not leaving from the same part of India in which you arrived, you won't have the hassle of trying to return the rental phone. Reputable service provides are Airtel and Reliance, there may be info on renting or buying at http://www.airtel.in/ or http://www.rcom.co.in/Rcom/personal/home/index.html , see esp the Prepaid Mobile section on Reliance which has a store locator as well.

Either Airetl or Reliance may have counters at your arrival airport; if not ask at your hotel for the nearest shop. If you are travelling to other states, it may be cost-effective to have different SIM cards for each state; however rates are rather low (compared to the US esp) so it may not be worth the time and trouble to get a new SIM card for each state.

In most cases when buying a SIM card or a phone in India you will need to show a passport and fill out some paperwork, so bring your passport with you.

Most require a visa size photo. Bring a couple if you are going to buy/rent a phone or even if you're just buying a SIM card. Ask your gadget loving friends if they have a phone you can borrow so you only will need a SIM.There is a booth at the airport where you can buy them, or go to a phone store. Airtel is good.
If your friends have their last (perfectly good) phone available for you to use, just check to see that it has multi-band capability. I forget what frequency band India uses (850? 900?); your local carrier can tell you.

I was there in January, paid $25 for a brand new unlocked Nokia, another few $ for Sim card. With those prices, no point renting.

We took unlocked phones from Australia and just went to the local (cuboard sized room) Vodaphone agent and he organished it all for us. You will need a couple of passport photographs and will need to fill in some forms. The agency if you are kind enough to him, will do this for you. You will however also need an Indian address.
The phones worked fine for us. There is a number if you need to add more money. We just took the phones back to the agent and got him to do that between our trips to and from Delhi.

Can you use the address of your hotel?

We will be needing an Indian cell as well. Hoping that the trip planner we use will provide one. If not, we prefer to get a SIM for an unlocked Blackberry or rent a phone before our trip. Does anyone know how to accomplish this? (We can't buy or rent a phone there, because Mr. Crosscheck has a track record of spending all day in Vodaphone stores, wasting precious sightseeing time.)

As mentioned above, if you can't borrow one from a friend or work colleague, you can rent a phone or Blackberry in the US for international use from Cellularabroad see http://www.cellularabroad.com. Your current service provider may also rent international phones.

Your current mobile phone of course will also work (I can't imagine it isn't already mitl-band, check the specs); it will just cost you more to call. Check your international calling plan (or sign up for one for a month) to see how much that really will be. If you only plan to make limited interntaional calls and a few local ones, it may be not really be that expensive to just stick with your own phone. Given the time difference, you may not make as many international calls to the US as you think.

If you have a Blackberry, check about its international plan; again there should be one and it may be quite cost effective if you don't include calling; just messages. Your plan may already include international messaging. I don't think there is any issue with a Blackberry not working in any country other than Japan which uses a different system (and some models even work there as well).

You can also always use local email service (and Skype) in hotels and internet cafes to stay in touch.

Just take your unlocked phone with you and go to the vodaphone shop. They will need 2 photographs of each person who wants a SIM card (if you have more than one phone) and an Indian address (your hotel will do) and copies of your passport. Sometimes they also want copies of your driver's licence. If you go to a local vodaphone shop it is likely to be small and crosscheck wont have anywhere to "spend all day in".
These tiny cupboards of a shop barely have a chair for the vendor let alone anyone else.

We will be travelling in Uttar Pradesh, Rajasthan and Gujarat. Can anyone recommend the best service provider through all of these areas? Our preference would be to stick with one sim card and company.

Renting a mobile phone in this day and age is not a good idea. That's why there are very few companies that offer mobile rental. It's a DEAD business. As cheap as unlocked phones are, like others said, just get unlocked phones on amazon, ebay, etc. and pick up a sim card when you get to your destination.

India's cell coverage is excellent all over. The only issue might be refilling your card, so i would go with one of the big guys, like AitTel. They have shops all over, as well as a good 'call in" method of refilling.

Carobb - Just get your Australian phone unlocked before you leave. I don't think you will have any trouble with either Reliance or Vodaphone's SIM cards they are generally useable everywhere. The trouble we had was with the dongle we bought from Reliance for the laptop. Although we were assured that it would work in Rajasthan, it did not, other than Jaipur. Hence we never did use up the amount of download we had purchased for 4 weeks - a bit of a waste.
Also in the countryside, the phones tend to operate better outside a building rather than inside.
Don't forget to take a couple of adaptors with you. You will not be able to purchase them there. Hotels very occasionally have one or two for you to borrow but generally not.

Please forgive me for hijacking this thread - we haven't quite figured out our itinerary yet, but we might start off in rural areas rather than in a city where we can purchase SIM cards. (Plus Mr. Crosscheck will find a reason to stay in a Vodafone shop all day, even if it is the size of a cupboard.) Does anyone know if we can buy the SIMs in the Mumbai airport at 12:30am? Still would prefer to rent a phone.

I can't recall with certainty whether you will find phone shops in the arrivals area of Mumbai airport. There are some shops as you walk out along the long hallway after Baggage Claim/Customs toward the exit, but I don't remember if any of these are phone shops.

If you are landing in Mumbai at 12:30 am you are going to be staying overnight in Mumbai in any event, so the first thing you can do in the morning is look for a phone shop. No matter where you stay in Mumbai, there should be some sort of phone shop not too far away, your hotel should be able to advise.

If you really want to rent without buying a local sim card, then look at Cellularabroad see http://www.cellularabroad.com/.

In my experience, even in somewhat rural areas you will find phone shops. Many people in India have cell phones, even (and especially) in the countryside where the infrastructure for land lines never existed and is not being put in at this point.