Generally speaking, what you want is a monitor with an IPS (In-Plane Switching) panel, which is the type that Apple uses in their displays to get such vibrant and accurate colors, but suffers from slightly slower response times and generally higher cost. Most cheaper monitors available today are TN (Twisted Nematic) which are known for their quick response times and poor color reproduction and downright terrible viewing angles. PVA (Patterned Vertical Alignment) displays are less common and typically have very good contrast, but relatively poor viewing angles; some models have excellent color accuracy after calibration, others do not, so it can be a mixed bag in general.
As for what manufacturers to look for, LG and Hitachi are the big names that made IPS technology what it is today; Hitachi invented it, and LG continues to refine it. LG panels are used in a lot of the displays seen today made by several different manufacturers, including Apple itself. Other brands to look at (besides LG itself) include Dell, HP, NEC, and Eizo. There are others that also manufacture IPS displays, but the ones mentioned before are the safe and reliable brands that come to mind. Not all IPS displays come calibrated well from the factory, so adjustment will likely be required for accurate color representation.
LED-backlit displays also tend to have better color properties than the more traditional CCFL-backlit displays. One need only put a last-gen 24" iMac next to a 24" Cinema Display at the same brightness (actual brightness, not the brightness setting in OS X) to see the difference in color depth. However, Apple LED-backlit displays seem to use plain white LEDs, while some of its competitors use combined red/green/blue LED backlights to get the most out of the RGB spectrum, with spectacular results. Overall, however, this seems to be a very rare feature except on some of the most expensive models.
Unfortunately, it is infrequent that a manufacturer will list the panel type in the specs, and it can be very difficult to tell when browsing online. It is recommended you do some online research for model you're interested in to find out what type of panel it uses. A general rule of thumb, however, is that IPS displays are markedly more expensive than otherwise comparable TN displays.
P.S. Don't fall for the claims of "Dynamic Contrast Ratio". The numbers generated have almost no bearing on the actual contrast ratio of the display, and are there purely for marketing purposes. In fact, it's best to disable this option on such displays whenever possible for the best picture.
I hope this helps!
P.P.S. You might have been able to find plenty of relevant information if you had taken the time to use the forum's Search function (upper-right hand corner!).
EDIT: After digging around a little, I found the HP LP2475w and Dell U2410 monitors, both of which are much cheaper than the Apple 24" Cinema Display, and have many more features. The only thing they lack is LED backlighting, which is an uncommon and expensive feature as it is, so no big deal there. These seem to be the best monitors of this size for the price. If absolute accuracy is more of a concern than cost, though, I would suggest looking in to an Eizo or NEC display.
