No, don't prune orchids. Don't prune stems, don't prune leaves, don't prune roots. They are slowly growing plants. Pruning will set them back.
Many Dendrobiums (Den.) may flower in future years from old stems. Leave them on the plant until they turn brown and dry completely.
Den. nobile types are brought into flower at any time of year by manipulating temperatures in the grower's greenhouse. Six weeks of cool night temperatures (12C or lower) usually does the trick. They normally flower in early to mid Spring after a cool winter.
People divide large plants when they outgrow the space, but this isn't considered pruning.
At least some of those look like normal growths from the base. Don't divide those; that is where next year's flowers come from.
Take a look here for information on how to grow this kind of Den.:
Yamamoto Dendrobiums: Caring
Yamamoto Dendrobiums: Hints