V4s have really bad instability problems because of the way the pistons are set up. Two pistons at the front of the engine are always at top dead center when the front two are at bottom dead center. This makes the engine shake, the vibration needs to be countered with a heavy counterweight attached to the front of the crankshaft, which reduces the size and weight advantage of the V4.The spinning counterweight is called the harmonic balancer.

Everything except the straight-6 And V12 engines have inherit instabilities in their design and they require harmonic balancers to keep the engine from shaking itself apart. The straight-4. Is more stable than the V4, but it also needs a harmonic balancer to keep it stable. Larger displacement engines require larger balancers, so there is a point of diminishing return. Why swing a big counterweight to stabilize an engine when you can take that same mass and add two cylinders to the engine and get more power? 

@kesterpaul62, that's close but not quite accurate. The V4 was a Ford engine originally developed for the stillborn Ford Cardinal that was intended for the U.S. market and then repurposed for production and sale by Ford of Germany. The V4 was most definitely a 4-stroke engine. It was quite conventional aside from the configuration which was designed for a longitudinal front-drive layout, so compactness was a primary consideration. A single balance shaft was employed in its design to mitigate some of the inherent imbalance.

The Ford Cardinal was actually ready to roll off the production lines in Kentucky in the summer of 1962, but Ford pulled the plug at the last minute. Apparently they believed that a front-drive V4 small car would be too radical for American tastes. (They were probably right.) Also Ford was selling as many of the ultra-conventional Falcons as they could push out of their factories. So, everything was shipped off to Germany and the Cardinal became the 1962 Ford Taunus. The engine was later expanded to become the "Cologne" V6.

So what about Saab? The 2-stroke "overhead fanshaft" engines that you and Scotty are talking about were actually 3-cylinder inline engines, based on the DKW Auto Union engine. (That company became Audi.) As the 1960s progressed the limitations of Saab's 2-stroke design were becoming more apparent. Lacking the resources to design their own 4-stroke engine, Saab went shopping and found the Ford V4 to be ideal for their purposes. It became available initially in the 1967 Saab 96, and was also used in the Sonett sports car the same year as well as the 95 station wagon. The 2-stroke engine was finally discontinued in 1968 due to emissions standards. The Ford V4 continued to be used in the those older Saab models through 1980 when those were finally discontinued.

In 1968 Saab introduced the 99, which used an inline 4-cylinder engine co-developed by Triumph and Saab. It was initially built by Triumph and ultimately (after being brought in-house by Saab and with a lot of redesign to get rid of British Leyland quality problems) ultimately became the Saab 2.0 through 2.3 Turbo engines. The 99 was also the basis of the "classic" 900 that was hot stuff in the 1980s. But that's a whole other story.

When Saab was in business, they made a V4 engine. It was a two-stroke motor; oil and gasoline. It was a weird experiment that Saab has created.