Recommendation letters are a critical element of every application. They validate the claims you've made as an applicant, providing specific examples and details of your academic accomplishments, personal endeavors, and character. Selection committees rely on them to impartially evaluate your performance and potential to be successful in the opportunity you are pursuing. Good letter-writers are those who know you well enough to provide these assessments with enthusiasm and authenticity.
Academic letters are typically written by faculty, lecturers, or faculty research advisors who have overseen your work in courses, research settings, or other academic contexts. These letters generally address how you performed, your potential for future success in the field, and any other attributes that make you qualified for the particular award. Post-doctoral associates/fellows and graduate students may also have insight into your performance if they've worked with you in a course or project. However, depending on the fellowship or research opportunity, they do not usually make suitable academic letter-writers. It is important that you check the criteria of the award and/or check-in with administrators who manage the award to see whether letters from non-faculty members would be appropriate for that opportunity.
Some students, especially those in their early college years, have not yet had the opportunity to directly interact with faculty – perhaps you have had more direct interaction with Teaching Fellows ("TFs"). In these cases, you might consider asking the faculty course leader or head of a research group to work together with your TF to generate a co-signed letter. Keep in mind, though, that coordinating co-signed letters takes more time than usual, so plan ahead. Peers (other college students or recent alumni in student organizations), on the other hand, are not suitable letter writers. If you're applying for a non-academic opportunity, or one that is specifically interested in learning about the applicant's personal attributes (character, leadership potential, commitment to service, etc.), then you might consider asking for a letter of recommendation from a College staff member or organization supervisor, coach, faculty who may be familiar with your work outside of the classroom, work supervisor, or Resident Dean or other House staff.
Letters from high school teachers or your high school years: Soliciting letters from high school teachers is not usually acceptable for fellowship and research opportunities at the college level. However, there are some exceptions to this rule. If you've engaged in research as a high school student and are applying to a competitive research fellowship that funds independent study (e.g. Herchel Smith Harvard Summer Science Fellowship) as a first-year student, it may be acceptable to provide a letter from that experience, but only if the writer can provide strong evidence that you are qualified to pursue an independent research project.
Letters of recommendation are a critical part of academic and professional development. If you need a letter from a faculty member, research advisor, or other Harvard community member, do not be afraid to ask if they'd be willing to provide you a strong recommendation letter (even if the deadline is still years away, for instance, a medical school/graduate school application).
Regardless of the outcome of your application, be sure that you let your recommenders know you appreciate the effort and time they put toward the recommendation and update them on the outcome of your joint efforts. Even after the experience is long over, do your best to check-in with those recommenders; keeping them engaged with your trajectory is the best way to keep them engaged as your advocate and mentor.