I'll tell you what can't be transported, holographic material. Uncoupling those heisenwhozeewhatsis compensators didn't work. 
Seriously though, in The Most Toys we see a substance that's too unstable to be transported. Data had to ferry it from Fajo's ship to the Enterprise.

Seriously though, in The Most Toys we see a substance that's too unstable to be transported. Data had to ferry it from Fajo's ship to the Enterprise.