Most folding bikes are marketed based on their advantages for travel. It's certainly true that a combination of mass transit (a train or a bus, for example) and a quick folding bike like a Brompton or Bike Friday Tikit can prove to be a great solution for daily commuting. And if you frequently travel by air, buying a folding bike like a New World Tourist or a Pocket Rocket that can pack safely and securely into a standard-sized Samsonite suitcase is a much more satisfying use of dollars than spending money on the outrageous fees many airlines charge for transporting a full-sized bike these days.
While the above reasons are good and valid, over the past few decades of riding and owning a wide range of folding bikes I've come to appreciate some of the less obvious features of these unique machines. Some of these aspects may be drawbacks in one context, yet prove to be a surprising advantage in another. For example, let's talk a bit about wheels.
Most folding bikes use 16" or 20" wheels. If you want a folding bike with larger wheels, Montague makes some fine ones or you could get something built with S and S couplers or the lovely Rinko Travel System. Larger wheels, as any 29er mountain biker will tell you, tend to hold speed better and cope better with rough conditions. The bigger wheels have more angular momentum when moving, more inertia when stopped. Smaller wheels accelerate and decelerate quicker. As someone whose ridden damn near every bike wheel size made, I sum it up this way: "Big wheels are fast, but smaller wheels are quick."
For urban riding, small wheels are fun. BMX riders know this. It's easier to flick the bike around. That's not to say you can't do long distances with smallish wheels, hell I rode both Paris-Brest-Paris and London-Edinburgh-London a Bike Friday New World Tourist and never felt hindered by the bicycle, but you note the advantages of nimbleness more in stop and go city riding. In some places, like urban Japan, Mini Velos are popular. While mini velos don't fold, they do take up less space than a full size bike. And mini velo fans will attest to the fun factor inherent in smaller wheels.
Another advantage of the folding bike in a city environment is theft resistance. Rather than leaving your bike locked up outside, you can fold the bike and take it indoors. Folding bikes fit in small spaces so they are a good choice for apartment dwellers.
While folding bikes aren't cargo bikes per-se, they are surprisingly good at hauling things like groceries. On every folding bike I've owned I've been able to sling a bag over the front handlebars for quick grocery runs. The space above the smaller wheels can be used for a load without really messing up the bike's handling.
Folding bikes tend to be adjustable in terms of sizing. Some, like my Bike Friday Companion, are very adjustable. This makes it a great bike if you want to buy one bike for a growing child or if you want to have a bike that is shared between a couple of different people. Folding bikes also tend to have a low step-over height which means they can be a good choice for folks with short legs or mobility issues that keep them off a diamond-framed bike.
Since folding bikes still aren't exactly common owning a folding bike means you'll get asked about it. If you're an bike enthusiastic extrovert like me, you'll see this as a plus. If you're a more private person, you should be aware of this as a potential downside of folding bike ownership. But in general bike-curious people tend to be good people so maybe getting asked about your nifty bike isn't too bad a thing.
For me, the main thing about folding bikes is that they are fun. Yes, they are practical, sporty, zippy and environmentally friendly but they are also just a great way to be out and about in the world. So even if you don't commute daily or travel that often, perhaps there's a place in your life for a folding bike.
