This is my 1st guide so please show so understanding.
I have played a lot 3 on 3 games and one thing I have noticed is that a lot of players play with non-caster champs... and Rammus is the best against them! Even though if there are casters in the opposite team we can change a little bit items and play with the same pleasure :)

Runes are typical for the tank - health, armor and magic resistance (MR). Additionally I have chosen Greater Quintessence of Swiftness for speed boost (escaping, chasing, etc). Moreover movement speed in 3 vs 3 map is important for gangs and help your mates can need.

Main tree is Defense one. We need survivability and Rammus is a tank. Guess I do not need to explain it.
Other thing is one point in - it depends which spell you choose (Ghost, Cleanse, Clarity...)
The 2nd tree is Utility because we get additional experience and other things useful in 3vs3.

Items sequence proposed is for the fight against non-casters (e.g. , , etc)

In case of 2 even 3 (or 1 very strong caster) casters the sequence should looks like this:
good for first blood -> -> -> -> -> -> instead of Dorians shield ->

It is not all, guide is still in progress, nevertheless I hope it help you score some good kills and games!

To be continued.... :)