Yesterday, Google's Matt Cutts posted a video answer to the question "If I have 20 domains, should I link them all together?"
The short answer is, most likely no - you should not link them all together.
As I explained at Search Engine Land with my article titles Google's Matt Cutts: Linking 20 Domains Together Likely A "Cross Linking Scheme" - it may be considered by Google as a cross linking scheme - at least those are the words used by Matt Cutts.
Here is the video:
As you can see, the overall theme and feeling you get from Matt is that it is typically a bad idea.
So the next question I will hear is what about linking 18 sites, or 15 sites, or what about 10 or 5 sites together. I love those questions. Those asking those questions are linking the sites for one purpose, ranking.
So what about it? :)
Forum discussion at WebmasterWorld.
Image credit to BigStockPhoto for circle of chains