Can't really say for others but the Finnish army. However, I strongly suspect there are strong similarities to the German practice at least.

If you're referring to the WW2 period, the only troops that used bicycles on a large scale were light infantry - the "jaegers." They were the most mobile troops, generally composed of the youngest and fittest (often conscripts still), who would be used as the most mobile reserve. During summer they'd use bicycles; during winter, skis.

The equipment carried was pretty much the standard infantry equipment: personal weapon, ammunition and belt kit, rucksack. Rucksack would be strapped to carrier rack. Most bikes had another rack welded to handlebars, this was supposed to be used for greatcoat or blanket.

I dimly recall Maxim machine guns being broken down and strapped to bikes as well. Heavier kit followed in trucks or sometimes horse-drawn wagons.

Here's a picture of two officers or senior NCOs with their bikes, though without much equipment:

http://www.ww2incolor.com/finnish_forces/01polkupyoratt.html

Here's the Finnish military bicycle with front rack visible. Similar bikes were used during WW2.

http://www.inttistore.fi/sa-polkupyora.html

Here's a picture of German bicycle troops advancing in 1941; the equipment is similar:

http://www.ww2incolor.com/german/bs_16_30_D399876s.html

Source for the rest: old Finnish army field manuals like Sotilaan käsikirja.