It's virtually impossible to mine blocks with a CPU full stop, and it is no easier to mine blocks without transactions.
But yes, it is possible to mine blocks with zero transactions, but then that would defeat the purpose of mining, which is actually to proliferate transactions and secure the network, and the block reward is a reward for their work, though miners seem to forget that... If enough people/pools mined blocks with zero transactions it would make bitcoin suffer and the value drop as a result of lost confidence in its reliability and whoever was mining them would lose indirectly due to the drop in value.
http://blockr.io/trivia/blockBlocks with 1 transaction: 84454