Let's get the technical explanation out of the way first: A transverse engine is an engine mounted horizontally in the engine bay so that the engine's crankshaft axis is perpendicular to the direction of the vehicle's travel. Conversely, longitudinal engine crankshafts are positioned parallel with a car's direction of travel.
The non-technical way of explaining transverse and longitudinal engine mounting is that the shaft poking out of the engine and spinning really fast (crankshaft) can be pointed towards the back of the car (longitudinally) or to one side of the car (transversely). A common drivetrain layout using a longitudinally-mounted setup is a front-engine, rear-wheel-drive car. That allows the crankshaft to be connected to a drive shaft that runs the length of the chassis, connecting to the rear differential and powering the rear wheels. A front-wheel-drive car doesn't need a driveshaft like that, so they usually use a transverse-mounted engine.
Typically, a front-engined, rear-wheel-drive car is a more performance-oriented layout and used in sporty, premium, or luxury cars. Front-wheel-drive has long been the less expensive layout, hence the rarity of front-mounted transverse V8 engines.
Chevrolet Impala SS (Ninth Generation)
The 2006 Chevrolet Impala was an inexpensive sedan but not the first Impala to be front-wheel drive. That ignominy is reserved for the eighth generation. However, Chevy decided the ninth generation needed a performance version, and the SS was the first front-wheel-drive Chevrolet vehicle to use a V8 engine. The 5.3-liter LS4 V8 was definitely not in the rental spec models, pumping out a torque-steer-inducing 303 horsepower.
However, even fitting a small-block LS4 into an engine bay not initially designed for it wasn't easy. The LS4 had to be adapted by reducing the size in certain places, having new attachment points, smaller pulleys and pulley cover, and the starter motor had to be moved. The Monte Carlo SS, Pontiac Grand Prix GXP, and Buick LaCrosse Super also used the same engine and chassis, so they also have transverse-mounted V8s.
Cadillac Allante
Cadillac's two-seater luxury roadster is a strange car. It was built from 1986 to 1993 and featured an Italian coach-built body from Pininfarina. You can guess that the design house that helped brands like Ferrari and Alfa Romeo create some truly stunning cars doesn't come cheap. Even more expensive is having Pininfarina craft the bodywork and then ship it to America using specially equipped Boeing 747s. That's understandable, though, as the Allante was designed to be Cadillac's aspirational model to compete with top players from Mercedes and Jaguar at the time.
Given all that expense, the cost cutting of using a shortened version of front-drive Eldorado frame is baffling. Our best guess is that Cadillac didn't think its customers cared about how it drove or would drive fast enough to find out. It also makes the fact it was chosen as the 1992 Indy 500 pace car particularly baffling. It started at $54,700 in 1987, which would be around $120,000 today.
Ford Taurus SHO (3rd generation)
The Ford Taurus SHO (Super High Output) has a special place in a niche sub-section of car enthusiast's hearts. And rightfully so, it could be quite the sleeper, particularly the ugly and less showy third generation that started production in 1996. It was the third generation that featured a 235-hp aluminum 3.4-liter V8 engine with cylinder heads by Yamaha and a block built by Cosworth. Unfortunately, the engine was plagued with problems, and it's believed that's why there was no SHO trim for the year 2000.
The enthusiasts that keep their third-generation Taurus SHOs alive are a dedicated bunch as the engine is shoehorned in there, and even simple jobs like changing the starter motor can take hours of work. The next generation went back to using V6 engines, and even better, Ford's excellent 3.5-liter Ecoboost V6 twin-turbo.
Lincoln Continental (1995-2002)
The Lincoln Continental was the car to buy if you were successful and wanted an American-designed and built luxury car. Until the 1980s anyway, when things started to slow down following the fuel crisis. In 1988, the eighth generation Continental went front-wheel drive and was powered only by a V6 engine. The ninth-generation shared a lot of the underpinnings of the eighth generation but gained a detuned (from the Mustang) 4.6-liter V8 for the front-wheel-drive platform.
The level of luxury was still there, but in 1997 features started disappearing as Lincoln stopped competing with just BMW, Mercedes and Audi, as Acura and Lexus showed up and forced Lincoln to drop prices. In 2002, Lincoln ended the Continental and didn't bring it back until 2017. The last generation was V6 powered and only lasted for three years before being canceled.
Volvo XC90 and S80 (First Generation/Second Generation)
Volvo has always enjoyed the lucrative US market, and in 1999 it was bought by Ford. The Swedish company didn't have a V8 engine, considered essential in a luxury lineup at the time, so Ford suggested it looked to Yamaha for a solution. Yamaha had helped Ford get a V8 into the Taurus SHO and obliged Volvo by developing a 4.4-liter V8 that would fit transversely in the first generation XC90.
A year later, it was also offered in the S80 sedan. Yamaha used the 3.4-liter engine for the SHO as a starting point as the 60-degree camber cylinder banks and balance shaft were already designed. Initially, the engine made 288 hp but was quickly upgraded to produce 311 hp.
Oldsmobile Aurora
Oldsmobile needed a flagship model in the 1990s as competition from the Japanese brands joined the Germans to bulk up the luxury market. The company understood that Japanese luxury brands were gaining traction based on reliability and durability. The all-new Aurora arrived in 1994, and to define it as a break from the previous Oldsmobile cars, it had no obvious Oldsmobile badging but did feature a new emblem based on the old-school "rocket" emblem. Oldsmobile was ill-fated, but the Aurora was a great car.
It was luxurious, technologically advanced, the ride was great, and the handling well balanced, despite being front-wheel drive and having a Cadillac Northstar based V8 under the hood. The 4.0-liter V8 engine used was renowned for its refinement, and the Aurora scored extra points for its structural rigidity. Despite being a unibody construction, GM had to use a truck frame crusher to test rigidity as the Aurora broke the original testing machine.
Lancia Thema 8.32
The second-generation Thema was a rebadged Chrysler 300. But the earlier Thema, built between 1984 and 1988, was a sport sedan using the same front-wheel-drive platform as the Saab 9000, powered by a series of four and six-cylinder engines. However, what we're interested in is the 1986 Thema 8.32 super sedan that was powered by a Ferrari Tipo F105L 3.0-liter V8.
The engine is a variation on the one powering the Ferrari 308, but it used a cross-plane type crankshaft rather than the flat-plane crankshaft, smaller valves, and a different firing order. The Thema 8.32 was a fast, expensive, comfortable cruiser but nose heavy compared with more sport-based sedans like the BMW M5.