It depends on what you're looking to do with it. Most open source LMS's have come from the Higher Education sector, eg. Moodle, Atutor, Dokeos, Claroline. They're all very good at working in that sort of learning environment - often using a social constructivist model of learning.
If you're looking for a more-typical corporate LMS, which is just about delivering and tracking content (far less effective in my opinion), then the only one I'm aware of is Docebo: http://www.docebo.org/doceboCms/
It looks like it ought to be very good. It's as easy to install as any of the others, but it takes a while to get your head around the way it works.
I'll echo the comments on Moodle. It is an excellent system out of the box. It is open source and there is a large community of people who create extra modules that you can add on easily if you need extra bits. If you have the inclination it is also not too tricky to make small modifications yourself if you really need to, or again get some help from the forums.
Hi Nat -
We are collaborating with Emerald Publishing with the open source social network system Elgg.
Try it for free at http://intouch.emeraldinsight.com/
Give me a shout if you want to discuss professional social networks
07771 99 87 99
and then there is Moodle - open source LMS too.
Dr. Anthony 'Skip' Basiel
Hi all - many thanks for your suggestions and help. All very grateful. I have looked into Moodle, and it does look great but it also seems quite tailored to academia. I like the look of e front as it is more enterprise based but I just cannot get the open source programme to install correctly which has annoyed me somewhat. Does anyone have any experience of installation who can assist?
Anthony - I will take a look at Elgg - many thanks!
Amanda - I work for a global PR company as an ICT Trainer and I'm looking for an LMS which will allow for me to build courses and also to record training for every user. Anything you can recommend?
Free! Now there's a nice idea .... So are you referring to something like Moodle which is open sauce - the claim is that it is free and schools for example, frequently choose it on the basis of that claim .... and then employ several technicians/designers who can manage it. One of the reason Moodle looks like its tailored to academia is because a) OU have invested in its development, b) academia uses designers/teccies to customise it so that it is fit for purpose .... get your own teccies/designers and it should work for you ... if you pay!