The flagellates are characterized by the possession of flagella: one or more (but rarely more than a dozen) long, mobile extensions from the cell. Unlike pseudopods, flagella have a rigidly-organized core of cross-connected microtubules that drive them. Flagella move in various ways: they may spin, or whip, or move like tentacles, among other things. They may carry extra structures, like bristles, or combs, or stiff sections, or a flat outgrowth of membrane that acts like a fin. Most flagellates are swimmers - being microscopic, they are not powerful swimmers, but many can get from place to place if the distances between are not very large. In humans and most animals (and more primitive plants), sperm cells are very much like tiny flagellates; again, humans have the genes to produce such forms.
Of the protozoans that have both animal and plant characteristics, most are flagellates - there are entire subgroups of flagellates that are considered algae. If you've seen ponds or lakes where the water was yellow-green or kelly green, that was probably from a multitude of flagellate algae (dark blue-green water is usually from a type of prokaryote). Flagellates are important parts of plankton, life that drifts near the surface of large bodies of water, where they form the base of many aquatic food chains and may be producing most of the atmosphere's oxygen.
There are several forms of flagellates that can invade humans and produce disease:
Giardia is a teardrop-shaped cell that has two nuclei beneath a bit of a cup-shaped depression and eight flagella - under a microscope it looks a bit like a cross-eyed short-handled racket. Giardia lives in the intestines of a large variety of animals, and seems to be able to pass between and survive in many different species, an ability which is not common in parasites (each species' digestive system is a unique type of ecosystem). In humans, the flagellates reproduce in the intestine and usually cause no symptoms, although the host passes drying-resistant cysts in feces, through which other hosts can be infected. Giardia is usually picked up from drinking water contaminated by feces from infected animals or humans. When humans do show symptoms, the disease is called giardiasis or beaver fever (it was connected to beaver ponds, which are popular watering holes and likely to be infected; it isn't known for sure whether beavers can actually carry Giardia). Upon introduction, these flagellates may go through an explosive phase of reproduction and coat the intestinal lining, affecting food absorption and causing immune responses that can lead to nausea, cramps, and diarrhea. Giardiasis is almost never life-threatening, and even if untreated, the symptoms usually pass within a couple of weeks - at that time, the protozoa are still in there and the host is still passing cysts, but the population is low enough to not bother the host anymore (without reinfection, though, the population in many people will dwindle to nothing eventually). And once in place, the animals effectively prevent reinfection from producing symptoms - it's a situation, again, where the "locals" can drink the water and be fine, but "tourists" (or returning locals who have lost their "buddies") are very likely to get sick from it. This pattern can be seen in a few other water-borne microbes, too, including amebas and bacteria. Hosts do not develop immunity to these parasites, mostly because immune reactions can't reach into the spaces of the digestive system - the surfaces are as far as they can go without being digested.
Trypanosomes are a particularly nasty parasite, with different species that can affect different hosts and cause a number of fairly different diseases. Trypanosomes use biting insects as both hosts and transport between vertebrate hosts. Trypanosomes can cause diseases in humans, but can also affect game species and livestock. In Africa, the parasites affect the nervous system, disturbing daily rhythms and sleep cycles - the disease (in two forms: chronic and acute) is called Sleeping Sickness (African trypanosomiasis). The victims have trouble both with sleeping and staying awake, and eventually fall into comas and die. The African trypanosomes use tsetse flies as their other, or vector, host - vectors are sometimes called carriers. In South America, a type of biting bedbug is the vector and the disease is called Chagas Disease. Chagas disease can take many years to produce symptoms, but the flagellates invade many of the body's tissues and cause irreversible damage. Often problems with the heart are the first (and worst) sign of trouble. It is quite likely, judging from descriptions of Charles Darwin's health in his later years, that he picked up Chagas disease during his trip on the Beagle, although he lived about 40 more years and didn't become ill until he was in his 50s. Trypanosomes have a feature that helps them to live in a host for long periods of time without being killed by the host's immunity: when invaders get into your tissues, your immune system recognizes that they don't belong by analyzing molecules on their surfaces and checking that against your own list of surface molecules (this is a huge oversimplification of what actually happens, but it will help you get the idea). Foreign molecules (whether on dangerous invaders or not), called antigens, are responded to in these steps: