There are many factors that influence the quality of a monitor - convergence, dot pitch, matching the graphics card to the monitor, running the monitor at its optimum resolution, and making sure that it is properly calibrated. There are other factors that are harder to judge without opening the monitor's case, such as how much shielding is used, how many circuit boards are used, how the wires are secured, power supply, etc. (NOTE: DO NOT OPEN YOUR MONITOR! There are high voltages inside a monitor that can kill you, even if it is unplugged!)
There are also a lot of factors that aren't very important. The number and layout of the OSD (on-screen display) controls don't really matter, as you shouldn't have to adjust things very often. The connector type isn't that important, either. In general, an integrated cable (one that doesn't unplug from the monitor) has the advantage of soldered[S1] connections that usually provide the best connection. BNC cables tend to be a little more robust than 15-pin Mini D Sub cables, but, because there are five separate connections, they can be a little tricky to set up. Also, they don't support Window's Plug and Play. There is virtually no visual quality difference between BNC and Mini D Sub connections. DVI connections are less prone to degradation and interference as the signals travel across the cable (not really a problem with good cables), but the DVI standard has not yet been extended to high-resolution monitors that have high refresh rates. DVI is mostly used for LCD displays that run at relatively slow refresh rates.
Multiple connectors, headphone jacks, built-in speakers, and the like can be nice, but they are mostly just frills, and have nothing to do with the quality of the image. Special glare reduction coatings are nice if you have a lot of light in your work environment, but almost all monitor manufacturers use the exact same coatings - the only difference is in the amount. Thicker coatings eliminate more glare, but reduce the amount of light emitted. If you have glare problems, it's probably better to try and change your lighting environment, rather than choosing your monitor based on glare reduction coatings. Power consumption also shouldn't be much of an issue as most CRTs only consume about 130 watts (LCDs consume about half that, but the higher initial cost of an LCD pretty much offsets any savings, in the long run).
Depending on your situation and the types of applications you run most often, different factors might be more or less important. If you do a lot of text work, note that shadow mask CRTs tend to give a sharper picture. If accurate color reproduction is more important to you, then an aperture grille CRT might be a better choice. If desk space is at a premium, then LCDs might be a good alternative though they are fixed resolution, and generally not well suited to video or animation. Flat-screen CRTs and LCDs offer the best glare reduction, but tend to be more expensive and heavier. Flat-screen CRTs also tend to suffer from geometric distortions at the edges and can appear to give a slightly concave image. Because of their design, LCDs have no geometric distortion problems, making them ideal for CAD work.
While it's possible to get an unusually good, cheap, off-brand monitor (or a lemon from a top-notch manufacturer), in general, you can expect to get what you pay for. Do a little homework, check the specs, read reviews, match the monitor to your system and preferences, and make sure you can exchange it if you happen to get a dud. You're going to be staring at your monitor for a long, long time, so it's worth getting the best you can afford.