Most small tube worms feed actively on bacterial aggregates, phytoplankton and suspended detritus, but unlike suspension-feeding corals, feather dusters generate their own flow to capture food particles rather than relying primarily on the flow of currents to bring food particles to them. These worms extend their feeding pinnules (the "crown" of the feather duster) and actively pump water through the pinnules to capture organic particles as they pass through the crown. Ron describes this in some detail in his article Segmented and Vermiform, it's a way of life....
Most people who keep tube worms generally try to target feed these animals to ensure that they get enough food in the aquarium, but most people are rather shocked to discover that the current is generated from the outside (bottom) of the tentacles as water is drawn upwards into the crown from underneath and expelled towards the center of the ring on the upper side. This is particularly important, because most people who try to target feed these animals have a difficult enough time because the worms withdraw into the tube as soon as they sense the current generated by spraying food towards them. But if you are directing the food towards the center of the crown, even those worms that don't retract will get little to no food from your well-intentioned efforts because the food will be blown away from the animal by it's feeding current (the center of the crown is where their waste water gets pumped away -- by target feeding the center of the crown, you're effectively trying to feed their butts as Staceon described). Actually, their mouth is really at that end and their butt at the other, but the waste water current ensures that they cannot capture any food directed towards the middle of the crown and you may as well be feeding the wrong end. Therefore, if you are trying to feed a feather duster worm, you should be directing the food to the side and below the crown, where it will be drawn through the feeding tentacles and feed the worm. By creating water flow through the feeding tentacles, the worms actually use the eddies generated by having a branch of their crown in the flow (similar to a rock in a stream causes a swirling eddy which pulls objects in behind the rock) to cause food particles to swirl around that branch and get captured on the upper surface of the tentacle.
Depending on the species of worm and how big it is, the "mesh size" through the feeding pinnules can be very tiny or quite large, and the efficiency of capturing particles of various sizes depends on how big that "mesh" of feeding tentacles is. Tube worms are very efficient at capturing particles of the correct size, and an undisturbed worm feeding at it's maximum rate can actually clear 100% of the particles of correct size (whether that is phytoplankton or zooplankton depends on the size of the worm) suspended in the water pumped through the pinnules. This is rare among suspension feeding marine invertebrates, and is particularly important, because that filtering efficiency is much higher than that of corals, clams and other animals that can also feed on suspended plankton, so, in general, tube worms should be the last to show signs of starvation given a lack of planktonic food -- if you have other filter-feeders, the chances are that they are suffering at least as much as your worm (at least assuming that they are trying to feed on particles of the same size)...
As I said above, most small tube worms feed on bacterial aggregates, phytoplankton and suspended detritus, but the very large species, such as Sabellestarte spp., tend to switch to consuming largely zooplankton as they grow. The small animals still feed primarily on bacterial aggregates and small phytoplankton (such as that from scraping your glass) in the aquarium, but as the animal grows, so does the size of the mesh, and therefore the size of the plankton preferred, and by the time the animal is an adult, these worms feed primarily on tiny zooplankton (rotifers, invertebrate larvae, copepods, etc.) but probably still capture large phytoplankton as well. The worms usually get enough suspended detritus and bacterial aggregates to grow when they are small, but as the animals mature and require larger plankton, the supply in most aquaria is quite limited, and specific feeding becomes ever more important. This is why many people observe that a worm initially does well in their tank, but as it grows it seems to languish and eventually suffer in the aquarium after long periods of apparently thriving. Feeding a variety of phytoplankton to small worms will obviously benefit them, but as they grows, the more zooplankton these animals will want in their diet, and the inclusion of rotifers will certainly be a good idea. This is also a possible explanation for why animals so often lose their crowns in aquaria aside from the obvious stress response Staceon described, it is also likely that large worms lacking sufficient food drop their crown to decrease the metabolic cost of maintaining it when the mesh size is incorrect for the available food. By dropping the crown and regenerating a smaller one, they both reduce the energetic cost of feeding (saving energy in a low food environment) and create a crown with a smaller mesh size to take advantage of the tiny particles such as bacterial aggregates that are more abundant in the reef aquarium.
For those people who cannot obtain or culture rotifers (I discuss rotifer biology and culture in RKGIZ #5), there are a variety of artificial plankton products now available to feed to animals which require these sorts of tiny prey, such as ESV's SDMP (which I discuss in detail in my original article and my updated follow-up in the Reefs.Org library), BSD's Rotifer Pearls or Artificial Plankton Rotifer (A.P.R.). The disadvantage of feeding prepared artificial plankton foods is that they usually settle out of suspension rather quickly, and are therefore easy to overfeed and contribute to a decline of water quality. Furthermore, few of them give exact nutritional profiles, so it is hard to determine just how closely they approximate the nutritional composition of the plankton they are supposed to replace. Even so, however, they are certainly better than starving the animals completely, and if you have no other options, by all means try a powdered plankton food.