No, Nemesis is not only the title of the Startrek movie that came out in 2002. It was the name we gave in 1983 to the hypothetical companion star that may orbit the Sun at a distance of a light year or so.
Briefly, we introduced the idea of a solar companion star to explain an apparent periodicity in the occurrence of both mass extinctions and crater formation by impacts on Earth. Independent of whether Nemesis exists or not, the danger of future impacts of asteroids and comets with the Earth is very real. For information about impact danger, see for example the NASA JPL site or the NASA Ames site .
Interestingly, our hypothesis keeps drawing new attention: it was recently featured in the book Nine Crazy Ideas in Science: A Few Might Even Be True" (I like the subtitle!) by Robert Ehrlich, together with hypotheses such as `Radiation exposure is good for you' and `distributing more guns reduces crime'.
The hypothesis that the Sun may have a very distant companion was put forward in 1984 in the article Extinctions of Species by Periodic Comet Showers by Davis, M., Hut, P. & Muller, R.A., 1984, Nature 308, 715-717. and independently in another article in the same Nature issue: Are periodic mass extinctions driven by a distant solar companion? by Whitmire, D. P. & Jackson, A. A., 1985, Nature 308, 713-715. A lively discussion started immediately, first in Nature itself. We posted there the following replies: Cometary Showers and Unseen Companions: a Reply, by Muller, R.A., Hut, P., Davis, M. & Alvarez, W., 1984, Nature 312, 380-381, and Terrestrial Catastrophism: Nemesis or Galaxy? by Davis, M., Hut, P. & Muller, R.A., 1985, Nature 313, 503.
The motivation for the Nemesis hypothesis came from the suggestion made in 1983 by David Raup and John Sepkoski that the last ten major mass extinctions had not occurred at random times, but instead showed a discernible periodicity. They quoted an average time span between extinctions of roughly 26 million years. At that time, it had already become clear that the K/T mass extinction, during which the dinosaurs died out, had been caused by an impact. Because the original idea had focused on an asteroid as the impactor, the logical task was to find a clockwork mechanism with a period of tens of millions of years that somehow involved perturbations in the orbits of asteroids. That was quite a challenge, given that asteroids have orbital periods of years, not millions of years. And although some modulation in these orbits will occur on much longer time scales, it was unclear how anything like a significant periodic disturbance could be set up on such a time scale of 26 million years.
It was only after we realized that comets will pose a comparable danger for impacts on Earth as asteroids do, that we found a possible solution. Many comets, in contrast to asteroids, move on orbits that bring them far out of the planetary system, into the Oort cloud that extends out to a distance of at least a light year from the Sun. If there would be a periodic disturbance on the orbits of such comets, a time scale of many millions of years would not be unnatural. This brought us to the idea of a companion star moving around the Sun in an elliptic orbit with a period of some 26 million years. Each time that the companion star would reach perihelion (the point in its orbit closest to the Sun), it would greatly increase the perturbations it would exert on the Oort comet cloud, thereby increasing the number of comets thrown into the inner planetary system. Therefore, soon after each perihelion passage of Nemesis the chance for impacts of comets on Earth would be significantly enhanced. For some recent developments, including tentative evidence of a higher cratering rate over the last 400 million years, see the work by Rich Muller's team on dating of lunar spherules.
Richard Muller has been engaged in searches for Nemesis. So far, these searches have not turned up any solar companion star. A complication in any search is the fact that we have no idea where in the sky Nemesis might reside: given the strong perturbations of nearby stars, there is no reason to believe that the star will be anywhere close to the ecliptic.
Fortunately, the question as to the existence of Nemesis will not remain open indefinitely: as soon as a repeated infrared all-sky survey will reach a positional sensitivity of an arcsecond, even a dim companion to the Sun can be discovered because of its lack of proper motion, together with its high parallax (at a distance of one or two light years, its parallax should exceed one arcsecond).
One of the criticisms of the Nemesis hypothesis was that passing molecular clouds might already have depleted the Oort comet cloud to such an extent that Nemesis would not have enough comets left to modulate their impacts. This argument was shown to be wrong in the article Have Interstellar Clouds Disrupted the Oort Comet Cloud? by Hut, P. & Tremaine, S.D., 1985, Astron. J. 90, 1548-1557.
A more serious criticism concerned the lack of stability of an orbit around the Sun with a period of tens of millions of years. Such an orbit would not be far from the sphere of influence of nearby stars, which would constantly perturb the orbit. Not only would these perturbations threaten to unbound Nemesis, they would also preclude a precise periodicity, long before they would disrupt its orbit.
This problem was addressed through a large number of simulations of different candidate Nemesis orbits in the article How stable is an astronomical clock which can trigger mass extinctions on earth? by Hut, P., 1984, Nature 311, 638-641, where I showed that all is well: even though the orbital periodicity will become noisy through the perturbations of other stars, in most cases the periodicity is still well preserved over the period of 250 million years for which Raup and Sepkoski originally fitted the timing of the last ten major mass extinctions.
A popular review of the Nemesis hypothesis appeared as Periodic Comet Showers: The Mainspring of Evolution? by Hut, P., 1985, in Encyclopaedia Britannica 1986 Yearbook of Science and the Future, pp. 46-57. For a more detailed early review, see Evolution of the Solar System in the Presence of a Solar Companion Star, by Hut, P., 1986, in The Galaxy and the Solar System, eds. R. Smoluchowski and M. Matthews (Univ. of Arizona Press). There I address the question of the orbital stability of a solar companion star in much greater detail. In addition I give some history there about the way the name Nemesis arose.
In a preprint version of our 1984 paper, we proposed four different names: Kali, Indra and George (the dragon-slaying Saint) together with Nemesis (cf. Nemesis by Rich Muller; Weidenfeld and Nicholson, 1988, pp. 114,115). While the first three did not survive the editorial pruning process of Nature, the name George did make it into Scientific American (Vol. 250, p. 68, 1984, in A Star named George). I prefer the name Kali for the same reasons as given by Stephen J. Gould (Natural History 93, No. 8, p. 14), who proposed the name Shiva. Unlike Nemesis, Kali does not only connote threats, but also life-giving qualities. This seems to fit with the double role of mass extinctions: after the disappearance of the dinosaurs, the mammals found themselves with extra playing room.