I've done some rough guesstimates of what I think this United India would look like. Remember, this isn't accounting for all the unborn generations of children from parents who died in conflicts with Pakistan and Bangladesh, and the economic data is based on the assumption that United India would be about as developed as the P.R. of China is today:
Name: Republic of India
Capital: New Delhi
Population: 1,493,223,514 (#1)

GDP (PPP): 12.5 Trillion (#2)
GDP (Nominal): 8 Trillion (#2)
Active Military Forces: 2,099,053
Reserve Military Forces: 2,655,821
Paramilitary: 1,668,486
Total Military Forces: 6,423,360
(Once again, I got the totals for the number of Military forces by adding the totals for India-Pakistan-Bangladesh. The armed forces of a United India could be smaller due to the lack of a Pakistani threat, or
larger due to India having more global commitments. Take your pick.

)
Judging by these (very rough) calculations, I believe that if India was united today, it would be (without a doubt), one of the most powerful nations on earth. China and India would be neck-and-neck (albeit with India
slightly ahead of China) and the West would become very anxious about the two of them getting involved in an armed conflict with each other. Chances are that, without Pakistan, China would be considered Public Enemy #1 in India.
Some other effects:
India might develop a "Sphere of Influence" comprised of Afghanistan, Iran (?), Bhutan, and Nepal
China and India would both be engaged in a game of one-upmanship in S.E. Asia. (Especially in Burma/Myanmar)
The Indian navy would be larger than IOTL
With a larger Indian navy, capable of greater power-projection, Somali Pirates might not be as much of a threat
China and India might have several "near-misses" over Tibet
India might become even more paranoid over the Maoist insurgency in Nepal, fearing that China is trying to use Nepal as a client or establish a Puppet in India's sphere of influence
The U.S. might do more trade with Democratic(?) India than Communist China
If China is India's primary enemy (as opposed to Pakistan), India might warm up to the US after China and Russia grow closer following the collapse of the USSR. This could mean we'd see F-16's and other American hardware in the Indian arsenal (Either that or India would have a home-grown arms industry

)
Indian Culture and Cuisine might see levels of popularity not seen since the 1960's
With more political stability and a higher standard of living on the subcontinent, there would likely be fewer Indian expats living around the globe, as they would likely stay in India
We might know more about ancient India than we do today, as a peaceful environment is more conducive to archaeology and anthropology