Nobody from my school has gotten into Harvard for the past 5 years, Stanford for the past 8 years, MIT for the past 5 years, Princeton for the past 4 years, and the list just goes on and on. Is this a bad sign for me should I apply to these schools? Granted, nobody that applied from my school was your extreme genius student that cured cancer or anything, but I thought that some of the rejects had as good a chance as other students from other schools that got in. So, do you guys think that these “admissions droughts” are anything to worry about for me?
Are you the valedictorian god you profess to be? 
Are you much stronger than the other applicants over the past few years? If there is no history of a connection between your HS and the colleges you mention, I do think it makes it a little more challenging than usual. No harm in trying but make sure your list is balanced with matches and safeties where you’d be happy.
Well, my first thought, which may be completely unfounded, is that whatever English teacher(s) is assigning college essays, proofing and “approving” them is not very good 
But seriously, it indeed may mean it’s a longshot for you. But it also means you could be the student to break the streak. The essay thing is partly serious, though. The droughts you mention make me think none of the applicants in the past many years have stood out enough to break through the noise. It’s become much more difficult to get into these schools, but you don’t have to cure cancer to do it. You do have to be interesting and make sure your essay and supplements reflect your unique perspective and what you might bring to campus. I’ve read some essays of students I was surprised to find out were going for Ivies–their stats were stellar but holy moly, their essays were a mess. And some were English teacher approved! The supplements matter.
So you’re saying that students have gotten into those schools in the past… I imagine some have had to settle for Amherst or Williams recently.
I suggest you should not worry about this, just like you should expect that even if your application is stellar then you still won’t have a great chance at these schools.
Instead, you should worry about why you have not cured cancer, and worry why your parents won’t donate $100M to each of these schools.
You know when I first start following CC, the high school that my kid was supposed to attend, the highest school was Cornell. That may explain why we moved, jk. But the school improved and the Val’s were admitted to Harvard and Stanford. I didn’t read Princeton yet. So I think you could be the first val to do that.
Apply wherever you want. You can’t do anything about your HS’s history with certain colleges so why stress about it. Admission to those schools are long-shots for virtually everyone (regardless of HS) so be sure to have a smart application list which includes match and safety schools as well.
There are almost 37,000 HS’s in the US; Harvard (as an example) targets a class size of 1660. Therefore, every year, there will be 35,000 HS’s that did not get a student admitted to Harvard.
Unless past students from your high school that were accepted have gone on to perform poorly at the university, or backed out of an ED acceptance for non-financial reasons, there is no reason to think there is a jinx on your school. All you can control is your own application. Good luck.