My experience with scholarships is that I thought they were a lot more important than they actually were. All of the colleges I applied to had "need-blind admissions", which means they decide whether to admit you or not without looking at how much you can pay. Then there's the financial aid process, which was based on a standard formula for how much you or your parents could afford to pay. All the schools used this formula, and then filled in the difference with financial aid.
Since I was not going to be able to afford to pay anywhere near the full price for any of the schools I applied to, I was going to get need-based financial aid anyway. Unless I got enough scholarships to more than make up that amount, then all the scholarships did was to decrease my "need" and therefore decrease the amount of need-based financial aid I was qualified for. And practically speaking, in my case, there was no chance at all that I'd get enough scholarships to fill my entire need.
Imagine for example that you're going to a school that will cost $25,000/year (tuition, housing, fees, living expenses) and the formula says you / your parents can afford to pay $5,000/year. That means you qualify for $20,000/year in financial aid. Now you get $5,000 in scholarships... so your "need" goes down to $15,000/year and the school only arranges $15,000/year financial aid for you that first year. You still have to pay the $5,000/year you can afford to, in addition to the $5,000 in scholarships you got.
Scholarships did matter somewhat. Need based aid is a mix of grants and loans. If you get scholarships, some of that money will reduce your grant aid, but some of it will reduce your loan aid. For example, maybe the school would've given you $8,000 in grants and $12,000 in loans, but now that you only need $15,000, they give you $6,000 in grants and $9,000 in loans. As a result, you have $3,000 less in student loan debt after you graduate.
Keep in mind that student loans don't start requiring payment (or charging interest) until after you finish college.
Basically, scholarships are good and help you out in the future, but I really shouldn't have stressed out about them nearly as much as I did. They did not at all affect my chances of going to college, paying for college, or my financial situation while in college. They did somewhat reduce my student loan debt after college, though not by a large percentage.
You might be in a different situation, of course. Perhaps you're applying to some schools that aren't need-blind admissions. Or maybe your family is wealthy enough that you're not going to get need-based aid anyway. Or you're going to schools that are so inexpensive that you can get enough scholarships to fill all your need and then some. Scholarships may matter more for you than they did for me. But these are the things you should look into to find out.