Choosing a pair of studio monitors

Sound!
This is the single most important part of it all. Get out there and listen to as many speakers as you can! Bring a recording you are familiar with. When you listen, make sure to ask the sales person to turn off all equalisation and signal processing, so all you are hearing is the speakers. Studio monitors and home speakers are not designed the same, because they don't do the same thing. Be prepared for real monitors to sound much more detailed, not really harsh, but a lot more in your face than home speakers.

Passive vs Powered
Passive speakers require an external power amplifier, while powered speakers have one built in. If you don't have an amplifier, powered speakers are a great choice because they are simpler to hook up, they take up less space, and the amplifier is matched to the speakers. Passive speakers are nice because they give you a little more flexibility, and you could even power them from a home stereo receiver. Most monitor speakers currently available are powered.

Connectivity
If you buy powered speakers, you need to check what kind of connections they have. Most have XLR, 1/4" and RCA jacks with a level control, while higher end monitors sometimes only have an XLR connector. Also, some monitors now have a digital input, which is usually a S/PDIF connection with an RCA or optical connector. If your computer interface or digital mixer has this kind of output, this may be a great choice for you. It's still nice when digital speakers have an analog input as well because it allows some flexibility if your setup changes or you need to hook your speakers up to something else temporarily, such as a keyboard.

Size
Generally, the larger the speaker, the more output it has, and the more bass it has. If you don't have a lot of room but require lots of strong bass, you may want to consider a subwoofer. Also, make sure the speakers you want fit where you want to put them! This is easy to overlook.

Magnetic Shielding
If your monitors will be close to a tube type computer or video monitor, make sure they are magnetically shielded. Even if you do get shielded monitors, they may need to be a little waise away from your monitor. This isn't an issue with flat panel LCD screens, only tube type monitors.

Frequency Response
You want the frequency response to be as wide and smooth as possible.

Hooking them Up
Get a high quality cable to hook your monitors up with, and try to keep it as short as possible. I recommend Mogami or Monster Cable for this.

Power
Keep the power cables away from the audio cables if at all possible, and plug your monitors into a power conditioner to reduce noise.

For my studio, I chose the Dynaudio BM5A. They were pricey, but after hearing a lot of studio monitors, I realized they were well worth it. The other monitors I have liked working with are Mackie HR824. Adding a subwoofer is a good idea, too, especially if you work with bass heavy material or film sound. Not having a sub will cause you to turn the lows too high in the mix, so small monitors without a sub is not usually a good idea. I really like the Mackie HRS120 sub.