I've been using BC for almost 6 years. I registered it after using a public beta for a few minutes, and have never looked back. What a pleasure to use, and it just keeps getting more powerful, flexible, and friendly!
I use BC differently in different projects, but almost every day it comes in handy. Here are a few examples:
1. BC is my main FTP client: web site maintenance, downloads, etc.
2. Comparing source file versions far more usefully than my VCS software can do.
3. Using the data viewer to compare database files of a user-maintained mailing list by first converting them to CVS (and thus seeing what changes have occurred in the interim).
4. A script to do a nightly selective backup to an external hard disk.
5. Selective synchronizing of source files for quick and dirty version control.
6. Copying photos from a flash card.
7. Checking CD backups.
Happy new year!