Getting scholarships to help pay for college is a common strategy. It can be a pretty good strategy for sure. I think that applying for scholarships is a great idea. If you can win any then its well worth the time and effort to try. I got a private scholarship from a regional chapter of the National Society of Professional Engineers Mine was $1,000 regional prize (20 years ago) and all I had to do was fill out an application, write an essay and do an interview. I had a 3.9+ GPA and I had won several academic awards in high school. Less qualified applicants didn't get scholarships.
It seems that I hear a lot of people who expect or hope that their kid will get some form of scholarship. Most private scholarships are based on merit and are highly competitive. Finaid.org reports that for 4 year college students "8.3% of undergraduate students received private scholarships worth $2,796 on average in 2007-08". That means that 91.7% of undergraduates got no private scholarship money. Very few students actually get academic scholarships. I would not expect most students to have any realistic shot at getting a merit based scholarship.
Of course there are exceptions where scholarships are little known or advertised and have few applicants, but I would expect that these are rare situations. There is little reason to think most free money would go unnoticed or ignored.
The NCES tracks data on student financing. Student Financing of Undergraduate Education for 2007 - 2008
Universities give out need based aid more than merit only aid. While grants from institutions were received by 19.9% of students, the institutional merit-only grants were received by only 8.8% of undergraduates.
"merit only grant" is another way of saying scholarship.
The universities giving merit scholarships are heavily weighted towards the more expensive schools. Universities that cost less than $6,000 to attend only gave aid of any form to 7.2% of students while universities that cost $19,000 or more gave aid to 43.2%. Often time the scholarships given by universities only partially reduce a high tuition bill. When I applied to colleges one private school in my home town awarded me a few scholarships. However even with the scholarships it was still more expensive than our state public university. I applied to some out of state universities and most of them gave me scholarships as well but none of them were affordable. In the end I went to my local public university with no scholarships and it was still the cheapest. Think of these scholarships at private universities like a 20% off sale at Nordstroms... its still more expensive than Sears.
The vast majority of students do not get merit based scholarships from private groups or colleges. If a student excels academically then they should certainly pursue scholarships, but students or parents of students who are only average students should not generally expect academic scholarships.