Bank wire transfers
Jeremy asks why banks won't help you figure out specifically when to transfer money so that it's sure to arrive on such-and-such a date. He compares FedEx and notes that they do a better job at solving this problem even though they're not in the business of moving money around. I don't know the answer for sure why this is, but I suspect it's for the same reason my online bill pay service makes me count backwards from the due dates on my bills in order to figure out the right date to send payment, rather than just letting me say "make sure my credit card gets paid $123.45 on April 16."
The reason is that banks don't want to be in this particular kind of insurance business. If you read the fine print of online banking agreements (likewise with wire transfer arrangements), you'll probably see lots of terms like "best efforts," "no warranty," and so on. They'll do their best to send the money on a certain date, but it's your problem if they don't, and it's especially your problem if it arrives later than you expected.
But FedEx is in exactly this kind of insurance business. For $13 or whatever it is they charge, they promise delivery on or before a certain date. If they fail, you get paid. If you want to get paid more when they fail (i.e., you're mailing a valuable item, or you just want to get paid more), then you can pay a higher delivery fee.
I don't know whether this answers Jeremy's question. In fact, my answer begs the question why banks aren't in this potentially lucrative business. I certainly don't know the answer to that, other than to cynically suggest that banks aren't willing to bet on their own reliability.

MBNA offers this... In a sense, for $12 their express service guarantees the bill posts the next day to your account. However, this is only their billpay service and is only valid for banks in the region where the card was issued.