Kush,
Please take my advice with a grain of salt, as it is likely to be controversial.
I disagree with the people who tell you to apply to 10+ schools. Personally, my thought is, if you don't get in to your 8th or 9th choice, do you REALLY want to go to school number 10??? I applied to only 6 schools and I was accepted to 4. Even if I hadn't been accepted into any of them, I would not have regretted this number, since these were really the only schools that I was seriously interested in attending.
Don't misunderstand me. It IS important to apply broadly (for example, pick a few schools you consider "first class", a few you consider "second class" and a few you think are good, but perhaps not stellar) to maximize your chances rather than applying to 10 Ivy League schools. I would certainly not put all my eggs in ONE basket. However, I think it's more important to pick wisely than to pick everything. Tailor your choices to ones you actually want to attend, ones with faculty whose research is in line with your own interests, and then concentrate on making QUALITY applications. I think in all honesty that if you make 8 applications and get rejected from all 8, that you probably would have been rejected from 18 as well. On the flip side, if you have an application that is attractive to potential schools, you will probably get picked up by a few if whether you apply to 6 or 60. I can't honestly understand how people find 15 plus programs that they actually WANT to go to.
One consideration that a lot of people do not make prior to making their applications is the financial side of things. Applying to grad schools is extremely costly. My undergraduate mentor suggested I apply to 12 schools. I was broke after applying to 5 and barely eeked out the 6th. To all the people who have the time and energy to apply to dozens of schools, more power to you. But, honestly, I wouldn't bother. It's way too expensive.
Like I said earlier, many others will disagree with me, and I invite you to take their advice seriously, as my experience is only one, and I would hate to mislead you.
Good luck with grad school and feel free to email me with questions.
Sarah