Hmm, this is all very interesting. I live in a densely populated urban city that aspires to be a big garden. (I'm not kidding here... any fellow Singaporeans or Singaporean residents?) My cycling experience has been very different from all those described here - I am told that my town (Tampines, if any local residents are reading this) is the only place where it is technically legal to ride on the sidewalk (a pilot experiment before they expand the ruling to the rest of the country or something), but I'm not sure what a difference that makes, since everyone rides on the sidewalk everywhere.
Bike lanes? Sort of - we have park connectors, which run parallel to sidewalks or pretty much serve as MUPs that are meant to link up major parks, but since the city is so densely populated, most of these run through major housing estates and effectively serve as pedestrian shortcuts or bike lanes. However, they don't always provide the fastest (or even straightest) path between parks, and are generally more relevant for longer distance rides - they're sort of like bicycle highways.
Mountain bikes, utility bikes and folders are most common. In fact, most bikes here are mountain bikes fitted with rear racks and/or baskets (I myself ride an MTB with a basket), though step-through and women's utility bikes are not uncommon. The prevalence of mountain bikes is probably because everyone rides on the sidewalk where one occasionally has to negotiate "rough terrain" - protruding tree roots, fallen branches and so on. (Not that the "terrain" is really "rough" of course - it's just that MTBs are best suited for it.) Pedestrians know what a bike bell sounds like, and will move for cyclists. Sidewalk cycling is pretty much a manner of life here.
On the other hand, road bikes for commuting purposes are very rare. Drivers are generally understanding to cyclists who need to cross junctions or zebra crossings, but not so to road cyclists who take the lane (quite possibly because there simply aren't many). Most road cyclists ride recreationally or competitively, but rarely for commuting or utility reasons.
Technically, one is supposed to dismount and push the bike across traffic junctions, wooden bridges and overhead bridges, but in my experience this is rare - I used to do so, but it became too much of a hassle in a pinch. Also, in some instances, it simply doesn't leave you with much cycling - if I dismount and push my bike across the overhead bridge near my house (which perhaps 30% of cyclists do, including myself), I only ride for about another 100m or so before I have to dismount again to push my bike across a wooden bridge (which maybe 40% of cyclists do, including myself).
As for dismounting at traffic junctions, on a regular ride, you might find two to three cyclists who do so. There was an incident a couple of years back when the Land Transport Authority installed metal blockades shaped like an upside-down U to prevent cyclists from crossing overhead bridges without dismounting, with the result that one unwitting cyclist from my town, cycling across the overhead bridge before dawn with little light, simply crashed into the blockade at his neck and was paralysed from the neck down. Our MP, bless him, blasted the LTA for the stupidity and they were removed.
I haven't been riding long, but these are my impressions of cycling in Singapore. Basically, it's PC heaven, VC hell.