MindMeister has received the most attention and deservedly so thanks to its slick interface and ease of use. The ability to embed the mindmap on your website/blog is very useful.
The free basic service allows up to six mindmaps with the premium and team plans allowing unlimited maps. Here is a comparison of each service.
Here’s an excellent screencast from DemoGirl.
Mind42 also allows collaborate mind mapping without anything to download or install. Everyone logged into the map editor will see changes in real-time too.
Here’s a screencast:
bubble.us offers less features and doesn’t look as nice as the others in this space, but there doesn’t appear to be any limits to the number of maps you can create and share online for free either.
So, if you aren’t all that into bells and whistles and a glitzy appearance, then bubble.us might be the one for you, especially for quick and dirty mind dump sessions.
You can’t go wrong with any of these services. Mindmeister is the market leader though.