Is it true that compressors are noisy? Can the noise be avoided?
All compressors, even the really expensive ones, have the potential to add noise. Most of them will add a bit of noise in normal applications. The reason is that compression reduces the peaks of your signal, which also brings down the average signal level. Our brains focus on the average levels, not the peaks, so reducing the peaks makes the whole signal seem quieter. To make up for that, nearly every compressor has a boost stage at the end, called "make up gain" (sometimes just labeled "level"). This gain stage boosts the level of the entire signal, including any noise that may have been in the signal path already from your pickups, preamp, pedals, room wiring, or a variety of other sources. You may not have noticed the noise before, but it was there- and the gain stage on the compressor just turned up the volume on it.
Additionally, any active signal processor may create a bit of its own noise, depending on how well it was designed and the quality of the parts used. So with compressors you get a combination of those two noise sources: noise that was already there in the signal, now amplified; and noise created by the actual circuit design and components of the compressor. That second noise source is where you can see improvement between a crummy cheap compressor and one of better quality. That's one factor in my reviews when I say a compressor has "low noise" or "more noise than I'd like". Good comps and bad ones will both amplify existing noise, but good ones are well-designed and made using high-quality components, and ideally should not add much noise of their own.
Now, to complicate matters a bit, there are many different types of compression circuit, and some types may be inherently more prone to amplifying noise. But it's hard to predict the results when shopping for a specific type of processor, as again it will vary depending on the way that particular model was built. Sometimes a comp may be designed to boost the high frequencies, which will result in more noise heard. Sometimes a pedal circuit will be sensitive to grounding issues anywhere else in the instrument-pedal-amp chain, resulting in hiss that's hard to solve. Some comps are designed with such low thresholds and high ratios that they can't help but boost noise a lot under normal use, even if the circuit itself is supposedly not noisy.
Another issue that I've run into many times is that some designs are very prone to picking up ambient electro-magnetic noise in the room. Tube compressors in particular give me endless problems this way. You may have a compressor that I say is "too noisy", but you don't hear any noise at all, and it's partly because you're in a different room, a different building and neighborhood, with different electro-magnetic fields.
Most often though, noise from any kind of signal processor is caused by ground loops or other grounding (earthing) problems. There is no universal standard for the way circuits/devices are designed in terms of grounding, which means that some devices which work great on their own, or with certain other gear, will work terribly in connection to gear which was just designed a bit differently. The ground/common of any one device is connected to grounds of all the other devices in the rig via several possible routes: the shield of the patch cords, the negative wire of non-isolated power lines, or metal rack rails for example.
Is there any way to combat the noise? Well, you can turn down the highs on your rig. You can eliminate other noise sources in your signal chain, such as overdrive pedals or any sort of extra amplification/gain/EQ/boost stages. You can put any noisy items after the compressor instead of in front of it. You can check for ground loops in your rig- they can be hard to track down, but ground loops are a major source of noise that most people do not even realize is going on in their system. Here is a very good article on that subject: Rane Note 110.
As a last resort, you can use a noise suppressor or a noise gate- but honestly I would strongly recommend doing what you can to reduce the sources of noise before adding any gear that will alter your signal even more. See this article for more about noise gates. Many people consider buying a rackmount compressor because certain models contain a noise gate as a feature, but this is a bad idea--the gate is a very poor solution to most noise problems.
Did somebody tell you that a compressor would help reduce noise in your rig? They were wrong! :-)