People say it's abuse... but honestly I sleep with books and read them near water, food, dirt, and the the like, and I have this strange habit of nervously tearing the margins, so dog-earing is the least of my problems. Anyways, if I didn't dog-ear, I'd probably bend it backwards (which even I, the book killer, think is a little harsh) or rip out th blank page in the back as a bookmark because I cannot seem to not lose a real one. *hangs head in shame SORRY BOOKS!
I don't like dog-earring my books, but I NEVER have a bookmark on hand! If it's a hardcover, I'll just use the dust jacket's sleeve thing to mark my page. Otherwise, I remember the page and take a guess later on.
I'm weird and don't dog-ear books and I also do my best to not break the spine on the books, at least not the first time through. And I generally don't use bookmarks either, I always try to end on a chapter so it's easy to pick up, otherwise I just do my best to remember what page/section I was on and try to find it again later.
Bookmark, or if the book has a jacket, I use the jacket flap (ie Harry Potter). Although, I do underline some books, which I definitely consider to be a sign of affection. I usually only underline the theory books I read for school, though.
I used to dog-ear books when I was little. Then my mum told me she always read from where she remembered, so I usually do that now. But since I started buying books myself, I've switched to bookmarks. Somehow, I can't bring myself to damage them... I also have tons of books that I sort of inherited and have underlined quotations, but I always keep a notebook where I write them down along with the page and line number ^_^
Something I do for books that I really love is make a bookmark that I leave in there in case I ever read them again. I painted a space ship one for sf books :D
I have my special bookmark, Avatar the Last Airbender trading card, but sometimes I dog-ear it if my bookmark is not available. I honestly don't think of it as abuse but I have had a few friends freik out about it.
I actually don't use either. I either remember what page I'm on (more difficult to do when reading at school) or I read until the end of a chapter. But, I do find Dog-earing (wait...what? I just turned that into a verb?) books to be a bad thing. Not really "abuse" per say, but damaging. I did that to a book once when I was little, and the corners kept weakening and would rip off the page. Since then, I mostly memorize page numbers.
Always a bookmark, even if it's just a scrap of paper. We call a tissue a "Grandpa bookmark" since that's what my grandpa always used. I'll use anything that's lying about: coupons, calendar pages, library passes...