Well i have had the dude for a while now, and for everyone to know :P so what does each hamachi star color mean? i have seen Green:Hamachi always tries to establish direct connection first and it is very persistent at this. While most of the connections take under a couple of seconds to establish, in some very rare cases it may take Hamachi up to a few minutes to complete the process.
When the connection is direct, the traffic flows by the shortest route possible and you are getting the best possible connection quality both in terms of the bandwidth and the latency.
About 95% of all Hamachi connections are of this kind.
Blue:High-speed relays are used to connect premium Hamachi users to their peers, premium or not. The upgrade to a premium level is a paid option and it also gives an access to a heap of other advanced features.
Yellow:Yellow or so-called unreachable status occurs when Hamachi cannot establsh direct connections between a pair of free Hamachi clients and these clients are set not to use low-speed relays.
Sparkling Green (it turns off and on):Blinking green indicator means that the peer is online and Hamachi is working to establish a connection. It typically takes under a second to establish the tunnel, but sometimes it may take up to few minutes.
If there're more, please tell me and what do they mean (and also tell me what those mean :D)
EDIT: Found the Sparkling One :P
EDIT2: Added what kash92 said 
EDIT3: Edited edit2 to add kash92 and not he
EDIT4: Corrected Spelling (i think)
