I have been up on my roof and have seen a couple of spots where the
shingles don't actually touch--I can see the paper that normally lies
underneath the shingles. Now I have not noticed any leaking or
anything like that, but I'm thinking that an ounce of prevention is
worth a pound of cure.

My options a I do have some leftover shingles in the garage, that
are much wider than these gaps. I also have a few bits and pieces of
older shingles that have come off the roof, that I have kept for
situations like this. Also, in the past, I have worked with Henry's
roof cement, a black sticky tar-like substance.

I'm wondering what would be the best product to fill in gaps that are
probably less than an inch wide, maybe 4-5 inches long. I'd rather
not use a whole, new shingle if I can avoid it. Are older ones that
have split up no longer good--would they be more likely to split up
again?