A number of projects have sought to build free software providing similar functionality to Lotus Notes. Many are coming from different directions, trying to replicate different base abilities:
A platform for customized client/server applications (Casbah)
A platform for collaborative computing (PINN)
A platform distributed modular workflow (Yoga)
A platform for distributed messaging (Citadel/UX)
Not unlike the story of the blind men and the elephant, each group of developers has a slightly different perspective on what is useful about systems like Lotus Notes.
There is a "spinoff" project of the Mnemonic Browser Project formerly called "Mediator" but now called Gather that seeks to provide similar "groupware" functionality to those provided by Lotus Notes and Netscape Communicator.
As such, it may be characterized as an attempt to provide high levels of interactivity, which would take it beyond the distributed data/replication/discussion group functionality in Notes.
This project is pretty much dead.
The Yoga Project is seeking to provide a more direct emulation of the functionality of Lotus Notes.
This project is in the design phase, and appears to be heading towards a more "direct" attempt to replicate the functionality of Notes:
Using RPCs or CORBA to split the system into modular components;
Distributed data replication using Sleepycat/Berkeley DB.
Note that nothing is preventing the construction of additional interfaces (say, via CORBA) to connect Yoga to Relational Databases such as PostgreSQL. Yoga nonetheless needs some "base" data store, and this ideally should be a DBMS that is small, simple, and fast.
Cryptographic components to provide security and authentication would presumably need to be produced outside the US.
Initial efforts are being directed towards development of the database portion.
The name was originally Gnuotes.
And here is yet another project building groupware "solutions." It bases things on a mature BBS system known as Citadel. (I rather think that Citadel predates the IBM PC...)
It uses the traditional sorts of BBS conferencing features to replicate "messages" from server to server, in a fashion reminiscent of NNTP.
Haystack - a user-oriented Information Retrieval system
Based on PostgreSQL.