Can contemporary technology simulate the spectrum of a star? The ability to manipulate light spectra (as in mercury lamps, sodium lamps, infra red) is within the ambit of contemporary technology. Stars are said to be unique in the spectrum they emit ; 
http://skyserver.sdss.org/dr1/en/proj/basic/spectraltypes/ writes to say

The best tool we have for studying a star's light is the star's spectrum. A spectrum (the plural is "spectra") of a star is like the star's fingerprint. Just like each person has unique fingerprints, each star has a unique spectrum.

with my limited understanding of physics, I may have understood wrong!!
Can contemporary technology simulate the spectrum of a star? 
 A: It depends how good of an approximation you want. If you just want something that looks like starlight to the human eye then it's not too hard - you can buy Solar spectrum bulbs at any hardware store. But of course, this isn't going to give you a great approximation, and it's only going to be anywhere close in the visible wavelengths.
If you want something that's going to be a fairly good approximation across a very wide range of wavelengths then just heat any random object up to between $3600\:\mathrm{K}$ and $50,000\:\mathrm{K}$, depending on the star. (Those massive blue stars at $50,000\:\mathrm{K}$ will present a challenge, but I think it's within the bounds of experimental possibility.) This works because stars and other hot object both emit spectra that are close to the ideal black body spectrum. You can get an idea of how close by comparing the curve on this graph to the edge of the yellow region:

(image source.) 
If you want to reproduce all those deviations from the ideal black body curve then it's going to be a bit harder, but it's probably doable if you have a good enough reason to bother. I would guess that a good technique would be to surround your black body with gases similar to the star's corona, in order to reproduce the absorption lines. Emission lines will be a bit more tricky, but I guess if there's no other way you could simply heat those gases up to the appropriate temperature.
The uniqueness of a star's spectrum comes mostly from its temperature and its composition, i.e. the gases that make it up, so by using this method you could probably more or less simulate the spectrum of a specific star.
This method would simulate the spectrum of light that the star emits, but if you wanted to simulate the spectrum that we actually see it would be much harder. This is because the spectra of distant stars are modified by a redshift, caused by the fact that distant galaxies are moving away from us. The redshift is basically the optical equivalent of the doppler effect, and it causes us to see frequencies lower than what the star emits. If you wanted to simulate this in the laboratory you would have to use a different method than the one I've described, such as the customised diffraction gratings described in Rod Vance's answer.
Of course, if you meant "simulate on a computer" then it's a different question. I think this is probably not too hard - you just need to look up the appropriate emission and absorption spectra and add them up in the right way. I'm sure people researching stars' spectra do this all the time.
A: I do not know explicitly of a technological solution to your problem, but I can in one sense give you an emphatic "yes" as long as the simulation were confined to certain wavelength bands. There may be difficulty simulating shorter than far UV wavelength behavior or longer than say $2\mu\mathrm{m}$ wavelength behavior with the technique I am about to talk about.
In single fibre optics, aperiodic gratings can realize reflectors and transmission functions with pretty much arbitrary wavelength response. There is quite a developed inverse scattering theory for designing such gratings for specific transfer functions. See the works of Leon Paladian in the mid to late 1990s on this topic. In particular, any causal, stable, linear, holomorphic transfer function can be realized by these techniques, so they could be used to mimic starlight in restricted bands by modifying the spectrum of a broadband or other source.
The kinds of things that this technique currently is good for are the following examples. Chirped gratings, where the grating is no longer periodic, can reflect different frequency components of the light with different delays (if the light first encounters high spatial frequencies, the blue components are reflected sooner than the red ones). So this kind of device can be used to cancel dispersion. This is of great use in communications, and also in femtosecond experimental physics, where a chirped grating can shape dispersed laser pulses so that pulses only a few femtoseconds long can be shaped. 
