I am looking for an instant messaging / chat application which can be used securely across different platforms, eg Windows, Linux, BSD!
Do any exist?
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http://www.cypherpunks.ca/otr/ is a plugin for several clients. I've used it with Adium on OS X and with Pidgin on Windows. It also works with Pidgin on Linux.
The greatest part of this is that it is protocol independent -- you can use it to secure conversations on Google Chat, Jabber, AIM, etc.
I personally use the mentioned plugin (OTR) for the pidgin IM client and several protocols, like MSN and GTalk - it even works with facebook chat. Both Adium and Pidgin are cross-platform IM clients.
It you feel more adventurous - or don't want to use public IM protocols (good idea), you can roll your own XMPP server and use any number of xmpp clients to connect to it. You can have ssl encrypted connections to your own server, and end-to-end encryption if you want on top of that (but that might be a bit unnecessary if you trust your server).
I've implemented an infrastructure like the above for use inside some companies: They wanted to use Instant Messengers for employees to talk to each other but at the same time restrict IM with the outside world: An IM server inside the company was a nice solution.
This depends pretty much on the protocol you want to chat in, e.g. IRC, AIM, XMPP, Yahoo!
Assuming you use Pidgin (an open source, multiplatform client), you can use the mentioned Off-The-Record (OTR) plugin.
If, however, you are more familiar with IRC, mirc (Windows only) has Mircryption plugin, while X-Chat (multiplatform) has FiSH plugin.
Basically, in any case, both parties must use the same application and/or plugin.
Disclosure: I'm the author of a pure Python FiSH plugin for X-Chat http://vithon.org/forum/Thread/show/54/FiSH_encryption_for_X_Chat_Python.html