My Brompton effectively has a stand built in: you can just swing the back wheel underneath, then it will balance wherever it is. I also ride an ambulance bike, and these all have side stands, which are very useful: if I'm called to a scene, I can just hop off the bike wherever I am (e.g. in the middle of the road), swing down the stand with my foot, and the bike will stay put. If there are several of us, we put our bikes perpendicular to the kerb (the same way motorbikes get parked) which is much more efficient than having a long line of bikes leaning against a wall.
By contrast, I did a cycle touring holiday in France last year, and the rental bike didn't have a stand; I cursed this on a daily basis! For instance, I'd sometimes be cycling along a road with downhill (grass) slopes on both sides. If I wanted to stop, e.g. to check the map or get some food from my panniers, I had to tip the bike over on its side, and I was always concerned about squashing whatever was inside. Here's a question for the "no stand" folk: have you ever ridden a bike that has a stand?
I now have a Roberts bike, and I explicitly said that I wanted a stand. I'm not sure about the brand, but it's a double-leg version (similar to the Pletscher mentioned above). Apparently this is more stable than a side-stand, because you don't have to worry about balancing the stuff in your panniers, although I don't know how true that is; I've seen a similar style on police bikes. The main difference is that you only get one wheel on the ground at the time; you can tilt it back and forth, otherwise it will depend on the weight, e.g. heavy rear panniers will keep the back wheel on the ground. If the front wheel is up in the air, it will then swing around, which I find annoying. The only way to stop that is to put the bike next to something, then turn the handlebars slightly so that the front wheel is leaning against the pillar/wall/whatever. However, if you've got a suitable place to lean the bike then you don't really need a stand in the first place! The only benefit I've got from the double-leg stand is that it can act as a work stand. For instance, when I attached a speedometer, I could spin the front wheel around (to test the signal/position) without having to actually ride the bike or lift it in the air. However, this is limited, e.g. I can't turn the pedals all the way round (they hit the legs) which means that this is no good for cleaning my chain.
For now, I'll stick with the stand I've got, but I'll probably replace it with a side stand at some point, and that's what I'd recommend to anyone else. I don't know about specific brands, though.