The center beam balance, for reasons that are likely already clear, is no more a part of modern science or commerce than is the Pony Express. Without this now-quaint machine, though, none of the scales in modern use would have arisen. A sampling of modern weighing machines:
Analytical balance: This is what you're likely to have seen in the lab. You simply place an object on a plate atop the unit and it returns a mass (or, if the user prefers, a "mass" in imperial units such as ounces or pounds). These are built so that the plate is at rest under the influence of gravity alone, and the machine balances this off by internally determining the force required to keep the plate precisely still.
Bathroom scale: Progressive advances in technology have resulted in models that are no longer anything close to a uniform bathroom scale definition. Most today are digital, but "old-school" analog models persist.
Counting scale: This is used to weigh multiple objects known to have a uniform weight (for example, precision ball bearings) and display a total piece count based on the result.
For example, if you had a large collection of different-colored but otherwise identical rubber balls, you could determine exactly how many are in your collection by loading them onto such a scale and setting the input parameter to the mass of one ball. Thus for a set of rubber balls weighing 0.125 kg apiece and having a total mass of 40 kg, the machine would respond that you have [40 kg/(0.125 kg/ball)] = 320 balls in your collection.
Crane scale: These scales have an expected capacity of 5,000 pounds (2,270 kg) or more, which is 2.5 tons, similar to most everyday motor vehicles. These are designed to weigh loads at the same time they are being suspended above the ground by a crane. This would not be an endeavor for the inattentive!
Microbalance: These can be read to a value of 1 microgram (1µg) or better. A microgram is one billionth of a kilogram, which means that while it's probably not a unit you have intersected with much on a conscious level, it's part of everyday life for chemists, microbiologists, pharmacologists and many other science professionals.
Postal scale: This kind of weighing device is an example of a computing scale, which displays price changes as mass is added or removed to suit customer needs. It is used to determine shipping weight or delivery charges for letters or parcels delivered by the United States Postal Service (USPS) or private shipping companies.
Vehicle scale: These scales are built for weighing large trucks, farm vehicles and other large industrial vehicles. You have probably seen signs that say "Weigh Station Ahead" if you have driven on U.S. interstate highways.
These are used to enforce safety regulations, such as ensuring vehicles using certain roads are not exceeding the posted weight limits of those roads – something, again, most people don't have occasion to peer at closely!