Update #1: According to ASUS' Twitter, the Android 4.0 update should begin rolling out in the U.S. tomorrow, February 24th. Yay!
Update #2: ASUS UK confirmed the same date.
After numerous delays and much confusion (mostly due to ASUS Singapore being more out of touch with reality than other regional divisions), ASUS finally started the Ice Cream Sandwich over-the-air update process for the original Transformer TF101 today.
The official ASUS Facebook account stated that the OTA with version number 188.8.131.52 is going to be available in Taiwan first, followed by other regions "soon after." Hopefully, that means the rest of the world will be able to enjoy ICS within the next few days, barring any unexpected issues.