I managed to snag a pile of white tri-fold diapers off of Freecycle a few months back. These make FANTSTIC burp cloths, because they're so absorbent, but at $1-$2 each new I'm glad I could get them used! (If you're not Freecycling yet, google it and find your local chapter.)
Three of the cloths were a bit stained in the middle, even after I washed them with bleach and the "sanitizer" setting on our washing machine so I cut out pieces of my favorite flannel, folded in the edges, and top-stitched them to the center sections.
When Ernie was a baby her Nana-Great sent three huge flannel blankets, that we used every day. (At least when they weren't in the wash.) Because they were so big, they made great floor blankets. And because Ernie was a champion spitter-upper, they made fantastic burp cloths. Seriously, I don't know how that child managed to put on SO MUCH WEIGHT. She hardly kept anything down! At any rate, my point is: the flannel is absorbent.
Here's Ernie, in all of her 4-month-old, 8-month-clothes, glory. Good gracious, look at those thighs! (Look at that- she's laying on a Nana-Great blanket.)