E.g., 今日 "kyoo", in which you can't break apart the pronunciation between the two kanji. Thanks!

I'm curious what you're up to with the kanji compounds? btw, your next post will be a cool 600th.

There are way too many of these to list. The technical term is 熟字訓 although "ateji" is sometimes used as well.

The very last section on this site has these kind of words that appear on the Joyo kanji liste:
http://www.mext.go.jp/b_menu/hakusho/nc/...01001.html

There's even some that are longer when written in kanji such as 海鷂魚（えい） and 　飯匙倩（はぶ）.

Not sure if it fits your meaning, but I remember 権兵衛 (ごんべえ) throwing me for a loop the first time I came across it.