Why do Indian citizens need many visas?

As one simple but quantifiable example, two of the conditions for a country to qualify for the US's Visa Waiver Program are:

1. Their Adjusted Visa Refusal Rate must be below 3%, and
2. The country must provide visa-free access to US citizens.

India fails on both counts:

1. The AVRR for Indian citizens in 2013 was 18.7%, 6x higher than required. This is worse than eg. Botswana (17.3%), although nowhere near the bottom of the pack (Somalia at over 75%!).
2. US citizens require a visa for India.

Being an Indian myself I can understand the frustration of having to apply for a visa for almost every country that you travel to. This Wikipedia article gives a fairly up-to-date information about the visa requirements for Indian citizens. As you can see, most countries that do not require an Indian passport holder to get a visa are in Asia and Africa. I think there are three reasons for your question

1. As @pnuts pointed out in his comment, all Indian national identity documents (PAN card, driving license, and even passport) are unreliable and do not meet the security requirements for identity documents imposed in developed countries like in EU and USA. You may be aware of how easily passports were being faked in India few years back. That is changing however.

2. India's own border control is not strictly enforced, which makes it easy for an illegal immigrant from neighboring countries to come to India, obtain a fake identity and then travel to some other country on a faked document. If caught, where would that person be deported to and who will take the responsibility? Definitely not the country the person traveled to.

3. Reciprocity. Internal politics are preventing India from reaching out. Countries that want to provide visa free travel to Indian nationals expect the same from the Indian government and opposition politics prevents it from taking the first step. I am hopeful that this may change in the current term.

It's a combination of a lot of things, but the 2 most important are:

1: Lack of reciprocal agreements

India has had visa barriers against foriegn visitors for a long time, stemming from a time when it didn't particularly want tourists. The national government was highly ioslationist/protectionist and only started taking down trade barriers in the 1990s for the most part.

If India makes overtures to other countries this will change but India has to make the first step.

2: Visa abuse/illegal migration by citizens.

Countries whose nationals have a history of illegal(undocumented) migration, or where access has been abused (Working illegally whilst on a tourist visa (or whilst visa free), overstaying, disappearing off the radar and never returning home, etc) are unlikely to be offered visa-free access until they have shown a committment to policing the problem, contributing to repatriation costs and start reducing the offending rates.

As an example of the reasons behind such things: New Zealand removed visa-free access to Thai nationals around 2003 because about 5% of "tourists" turned out to be sex workers - and being illegal, they were susceptable to manipulation by criminal gangs (Prostitution is legal in NZ, but illegal workers can trivially be ripped off on pay or held in disgusting conditions, etc, etc.) - after a substantial number of cases where Thai women were repatriated at NZ taxpayer expense or offered refugee status because they were unable to return home, visa barriers were erected to try and detect sex workers before they arrived and got pulled into criminal enterprises.

I've lived a number of countries where there are significant visa barriers to living/working elsewhere and the depressing thing is that the general attitude to compatriots working illegally in other countries is "good on them!" when the real attitude should be the opposite - it's those illegal people who are the cause of visa barriers - and if they keep doing it, the reason for various countries to enact further barriers for entry.

One might argue that making it harder to get a visa makes it more likely that people will enter any given country illegally, but that's not the way bureaucratic mindsets work. This is definitely one area where attempting to go around the rules has consequences for every member of the group.