I think that it's important to know how to compile a solid resume because resume writing is definitely an important life skill.
However, I don't recommend submitting a separate resume along with your college applications for the following reasons:
1. some colleges expressly tell applicants NOT to submit separate resumes;
2. most applications (including the Common Application) provide ample space for you to list your activities, accomplishments, and honors;
3. most of the student resumes just repeat information that is already set forth in the application;
4. some application readers find having to read additional materials annoying; and
5. many resumes are not read at all and therefore are a waste of your time.
If you do decide to submit a resume, make sure that the colleges to which you are applying do not expressly request that you do NOT submit them. Also - craft your resumes with care. Do not list the same activity/accomplishment more than once in order to "beef up" your accomplishments. Many students will list membership in "honor" societies under "honors" and "activities." Once is sufficient. "Double dipping" just makes your look bad. In my many years of interviewing applicants for Harvard, I found that having to wade through 3-4 page resumes only to find that the same activity was listed two, three and sometimes four times -- was a truly negative experience and duly noted on my interview report to the school.
Don't make it difficult for admissions officer to find out who you are. Keep it simple and direct and put forth your best efforts on the application. If you have the time to devote to agonizing over a resume, you have the time to craft an elegant application that sets forth the best version of you. Your application readers will be able to "get" you quickly and THAT is the goal -- right?