I upgraded to version 184.108.40.20619 of TortoiseSVN this afternoon. Shortly thereafter, any repository operations ended with a nasty little message box.
OPENSSL_Uplink(006F4010,05): no OPENSSL_Applink
Google turns up a hit on the OpenSSL FAQ discussing Win32 runtime library versioning pickiness, as well as a mailing list message describing a change in the SSL linking method for Tortoise.
So I decided to just to repair the install. Downloading the installer again, running it, and choosing the “Repair” option fixed the error after the subsequently required reboot. Done and done.