「ゆう」 is neither the kun'yomi nor on'yomi of 「昨」 and 「べ」 is not a pronunciation of 「夜」 either. The same can be said about the pronunciation 「きょう」 for 「今日」.
So how come the pronunciations of the two words are like those? If they are special, what was the origin of such pronunciations?
EDIT:
To respond to Mark Hosang answer on ゆうべ, from my dictionary software:
p/s: yup, the "sakuya" pronunciation is also there :)
The reading ゆうべ comes from the still-in-use word 夕べ（ゆうべ）, which apparently came from an old reading for 夕方（ゆうへ）(today usually read ゆうがた). The kanji are just "gikun" (義訓), that is, they're used for their meaning only and their reading is ignored.
The word 今日 was originally read けふ, which anybody who has read the iroha-uta probably knows. You can also still hear the old け today in the word 今朝（けさ）. It probably turned into けう and then into きょう in the various kana reading changes over the years.
The real pronunciation of 昨夜 is sakuya 「さくや」. ゆうべ is supposed to be written as 夕べ, but since they have same meaning, people just use the same.
今日 is read as きょう for normal everyday usage, but it could be read as こんにち or こんじつ when writing, and could sometimes mean "this days" or "on this era".
This is one of a few words that use kanji chosen purely for their meaning, rather than sound. Unfortunately, you just have to know about these words and not pronounce them as written. Fortunately, such words are rare.
Other examples:
