Any molecule that can exist as a gas under atmospheric conditions (e.g. in the lower troposphere, roughly 290K and 1 atm pressure) is a potential greenhouse gas if it is capable of absorbing infrared radiation. A molecule can absorb in the IR if a vibration of its bonds changes its dipole moment. (Explaining which molecules satisfy this criterion is rather complicated; try here and here for some rather technical information on dipole moments and their applications to IR spectroscopy.) One prerequisite is that there must be at least two different elements in the molecule, so diatomic gases such as nitrogen and hydrogen do not absorb in the IR and cannot be greenhouse gases. Water, however, does absorb in the IR (see its spectrum here).
Absorption in the IR and being present as a gas in the atmosphere is not the only requirement for a significant greenhouse gas. The molecule must also have a reasonably long lifetime in the atmosphere; some molecules might be chemically or physically removed in a very short time. Water vapor has a sufficiently long lifetime to accumulate, though of course it has a mechanism for removal (rainfall). Note that the amount of water vapor in the atmosphere is in equilibrium; adding more water vapor to the atmosphere will cause more rain, so the amount of vapor in the atmosphere is kept under control to an extent.
Another factor to consider is where in the IR the molecule absorbs. Compare the IR spectrum of water to this IR spectrum of the atmosphere. This spectrum indicates the ranges where water vapor, ozone and carbon dioxide (the main natural gases that absorb in the IR in the atmosphere) absorb. This spectrum shows that water vapor is responsible for a substantial amount of the natural greenhouse effect, the beneficial process that moderates the temperature of the atmosphere. (With no greenhouse effect, the average surface temperature of the earth would be about 0°C.) However, if you look at this spectrum, you can see that there are some ranges where the atmosphere absorbs relatively little IR. This is called the atmospheric window, and it is of great concern in studying climate change. If humans add gases to the atmosphere that absorb in this ‘atmospheric window’ range, we can add substantially to the greenhouse effect, by making the atmosphere absorb radiation in wavelengths that passed through the natural atmosphere. CFCs happen to absorb in some of these ranges, and so they are very significant as potential greenhouse gases.
One last thing to consider is the effect of human activity on the amount of the gas in the atmosphere. The amount of water vapor in the atmosphere from natural sources is large – so large, in fact, that water absorbs almost all the IR radiation that it possibly can. Adding more water would not produce a large change in the overall absorption of the atmosphere, particularly because water is in equilibrium and adding water causes more rain. The same is true, to a lesser extent, of CO[sub]2[/sub], but there is still cause for concern over that one. CFCs, again, are significant here because they have a very long lifetime (tens of years, at least).
To conclude, yes, water is a greenhouse gas, and it is an important contributor to the natural greenhouse effect that increases the temperature of our planet to a range where life as we know it is possible. Water added to the atmosphere by human activity is not likely to contribute significantly to climate change.