Radio astronomy involves a wide range of frequencies, covering the range from $\sim$10 MHZ to $\sim$100 GHz.$^{\dagger}$ With four orders of magnitude to work with, the most valuable band depends strongly on what sort of object you're observing, as well as what receivers are actually available on a specific telescope. Given the diversity of sources out there, it's difficult to narrow down the list to any small number of important bands, so this answer is far from comprehensive - my apologies to any extremely high-frequency spectral line observers out there. A truly comprehensive answer would be several pages long, so I'll forego that in favor of a briefer overview.
Spectral lines
The most well-known radio line is the famous hydrogen line arising from the spin-flip transition. Its rest frequency is approximately 1420 MHz, but as is the case with all spectral lines, extragalactic HI sources will show the line at significantly lower frequencies due to cosmological redshift. The same holds true for clouds within the Milky Way due to their motion relative to us, albeit to a much weaker extent. Neutral hydrogen is an important tool both locally (e.g. mapping the structure of the Milky Way) and for high-redshift sources (e.g. providing a handy tool for probing the early universe around the time of reionization).
There are four major hydroxyl radical lines between 1612 MHz and 1720 MHz, including the 1665 MHz line that led to the first detection of masers. They remain one of the key molecules detected in masing sources, and hydroxyl megamasers remain the dominant type of megamaser currently known. Notable, the hydroxyl lines lie on the opposing side of the water hole from the hydrogen line.
Carbon monoxide (12CO) has rotational transitions at multiples of 115 GHz, with the most notable lines being those at 115 GHz and 230 GHz (13CO also has a line near 110 GHz). They are quite useful for probing molecular clouds, meaning that CO surveys can reveal structures that might be absent on HI maps.
These are just a few of the key spectral lines in the radio spectrum; a 1991 National Academy of Sciences report came up with a far more comprehensive list of spectral lines of varying priorities. Formaldehyde, water (two more key maser molecules), methanol, ammonia, methine, and deuterium are all included, along with many others. Almost all lie between 1 GHz and 300 GHz (only two orders of magnitude!). An even more detailed list can be found here.
Continuum observing
Some broadband sources may be observed across several bands, and observations may take advantage of existing receivers often used for other purposes. For instance, the Arecibo L-Band Feed Array, or ALFA, included the 1.4 GHz hydrogen line and has been important for neutral hydrogen surveys (e.g. ALFALFA), but it turned out that its capabilities were also quite useful for pulsar searching (e.g. PALFA). Therefore, continuum observers might use some of the bands mentioned above, depending on available receivers and backends.
That said, different types of continuum emission peak at different frequencies, so we can certainly divide the spectrum up into chunks. The Handbook of Frequency Allocations and Spectrum Protection for Scientific Uses has some nice figures illustrating this on pages 13 and 14 of chapter 4. I won't reproduce them because I'm not sure about copyright status, but the gist is the following:
- Pulsars are the lowest-frequency continuum sources, observable below a few GHz. The 406-410 MHz band is often used, but again, 1.4 GHz receivers are also commonly used due to their availability. As pulse profiles sometimes show different features at different frequencies, it can be quite useful to observe the same pulsar in different bands.
- Supernova remnants (SNR) produce radio emission through synchrotron emission from relativistic electrons, and are actually visible across quite a wide range of frequencies (with synchrotron emission also in other parts of the electromagnetic spectrum). I'm not as familiar with radio SNR observations.
- The same holds true for radio galaxies, which are primarily detectable through synchrotron emission across a similarly large frequency range.
- The cosmic microwave background is a blackbody; at its current temperature of 2.7 K, it peaks close to 300 GHz, which again places it near the boundary of radio astronomy.
Protected bands and unusable bands
Many spectral lines (e.g. the HI line) lie in protected frequency bands in many jurisdictions, with widths which ideally take into account redshifts or satellite lines. Some key continuum bands (e.g. 406-410 MHz) have also received protection. Unfortunately, human activities are not the only thing that can make some portions of the spectrum unusable. For example, pressure-broadened oxygen lines in the 50-70 GHz range can be problematic. Water vapor, in addition to the strong line at 22 GHz, also produces strong lines at 557 GHz, 752 GHz and 970 GHz.${\ddagger}$
$^{\dagger}$Stricly speaking, there are indeed observations in the THz range, but at this point, the boundary between radio astronomy and infrared astronomy becomes a bit shaky.
$^{\ddagger}$See Essential Radio Astronomy by Condon & Ransom.
