Are there any twin engine aircraft without counter-rotating props?
Twin enigned aircrafts without counter-rotating propellers

A great many twins don't have counter-rotating props:

One such aircraft is the BeechCraft Baron 58, as seen in this YouTube video.

Another aircraft I can think of is the King Air 350.

It is not any more or less common to have one or the other. 

Contra-rotating propellers

Another interesting solution to the P-factor (prop pulling towards one direction), especially on single engine aircraft is contra-rotating props, two propellers on the same shaft that spin in opposite directions.

This is mainly for single engine racer aircraft, but there are multi-engine aircraft known to have it, such as the Soviet Tu-95 Bear bomber.

The pic shown here is a Spitfire Mk. XIV:



A better explanation of the P-factor

P-factor is the term for asymmetric propeller loading, that causes the airplane to yaw to the left when at high angles of attack.

Assuming a clockwise rotating propeller it is caused by the descending right side of the propeller (as seen from the rear) having a higher angle of attack relative to the oncoming air, and thus generating a higher air flow and thrust than the ascending blade on the left side, which at the other hand will generate less airflow and thrust. This will move the propellers aerodynamic centre to the right of the planes centreline, thus inducing an increasing yaw moment to the left with increasing angle of attack or increasing power. With increasing airspeed and decreasing angle of attack less right rudder will be required to maintain coordinated flight.