reg and wire were the original synthesisable types. Wires are constantly assigned and regs are evaluated at particular points, the advantage here is for the simulator to make optimisations.

wire w_data;
assign w_data = y;

// Same function as above using reg
reg r_data;
always @* 
  r_data = y ;

A common mistake when learning Verilog is to assume the reg type implies a register in hardware. The earlier optimisation for the simulator can be done through the context of its usage.

This introduces logic which can be used in place of wire and reg.

logic  w_data;
assign w_data = y;

// Same function as above using reg
logic r_data;
always @* 
  r_data = y ;

The type bit and byte have also been created that can only hold 2 states 0 or 1 no x or z. byte implies bit [7:0]. Using these types offers a small speed improvement but I would recommend not using them in RTL as your verification may miss uninitialized values or critical resets.

The usage of bit and byte would be more common in testbench components, but can lead to issues in case of having to drive x’s to stimulate data corruption and recovery.

Update

At the time of writing I was under the impression that logic could not be used for tristate, I am unable to find the original paper that I based this on. Until further updates, comments or edits, I revoke my assertion that logic can not be used to create tri-state lines.

The tri type has been added, for explicitly defining a tri-state line. It is based on the properties of a wire, logic is based on the properties of a reg.

tri t_data;
assign t_data = (drive) ? y : 1'bz ;

If you no longer have to support backwards compatibility Verilog then I would recommend switching to using logic and tri. Using logic aids re-factoring and and tri reflects the design intent of a tristate line.

Originally posted as a SO answer.