As a parent, I have learned that encouraging kids to have a growth mind-set is more important than outright praise. What do I mean by that? Instead of saying, "you're so smart!" or "you won!" say, "you worked really hard on that, even if you didn't get a good grad." This type of encouragement fosters the belief that a person's most basic abilities can be developed through dedication and hard work (instead of just innately being good at a subject).
Even if you have fostered this belief in yourself, you will usually never be the best at what you strive to do. This can be discouraging, especially when you're trying to convince yourself that you deserve a large fellowship or scholarship. That nagging voice in your mind might try to stop you before you even start, cutting you down by saying, "why even bother when there are so many more qualified people who should get this?"
But don't let the voice (which you have control over) squander your talents. You may never be the premier scholar or activist or teacher, but you have something unique to offer.
When I was writing my book, Funded!, I was about two months into the process when I saw on my friend's desk, The Ultimate Guide to Grants (or some such title). My stomach dropped but I asked if I could borrow it. This was pretty much the book I wanted to write, wasn't it? I sat with the book by my computer for a few days, feeling depressed, but one day I jumped into the fear and cracked it open. As I skimmed through the chapter headings, too nervous to actually delve into the info, I realized this wasn't the same book I wanted to write. This was about getting funding for non-profits. I had something different, and unique, to contribute to this field that was not addressed in the tome.
When you are beginning the process of looking into funding, your nagging mind might unhelpfully present more qualified applicants (I know a few of my outrageously extraordinary friends kept popping into my thoughts as I applied for my Fulbright). But come back to thinking about what makes you special and what combination of experiences give you a different angle than practically anybody else out there.
You may never be the best person to win a fellowship (or write a book), but something inside you deserves a chance to try. So remember the qualities that you, only you, can offer to the world.