They're secure enough that your everyday Joe won't be able to read what you've sent and/or received... Once they're deleted from your device, they can't be retrieved on the device either.
But the data is sent and received via Research in Motion's (RIM) servers, so law enforcement and related agencies can obtain transcripts if required, pending local laws and co-operation from RIM (which I imagine that would be all to happy to do, under the right circumstances).
As for the "whilst in progress" part, well your average Joe would be hard-pressed to see your messages (if someone cracks RIM's servers just to read your BlackBerry Messenger messages, well you're f@#$%d anyway because that takes some skill, B-I-G T-I-M-E, due to the fact that RIM's servers are notoriously secure!), but RIM should be able to see them and thus law enforcement agencies, again pending local laws...
The thing with computers and related technology is, regardless of how secure something is claimed to be, there is ALWAYS a "digital trail", you just need to know where to look and/or have the appropriate level of skill.
Anyway, unless you're doing something illegal, it's pretty unlikely that anyone will ever see your messages... There are ways to cover your digital tracks (or more accurately, minimize the possibility of anyone seeing your messages), though given the day and age we live in, it wouldn't be appropriate for me to divulge that information.