One of the ongoing questions for visual observers has been, “What can I observe that is still scientifically useful?” The answers to this have changed over the last decade, and will continue to evolve as conditions change.
You can observe whatever you want, of course. For many of us, observing variable stars is fun and addictive, and we’d continue to observe some of our favorite stars forever even if there were little chance of our observations being ‘scientifically useful’.
Although technological advances, and all sky surveys have intruded into what used to be the heart of the realm of visual observers, there is still a lot of room for visual observers to cover stars and events that are not being adequately monitored by automated telescopes and computers. The following is a list of suggestions based on the current state of affairs in variable star astronomy.
The Bright Realm
Very few of the all sky surveys monitor stars brighter than 8th magnitude. Most of the surveys that will come online in the near future will survey the sky fainter than 16th magnitude, so this fruitful area of visual monitoring will last for a long time into the future. There are literally hundreds of Miras, semi-regulars, Cepheids and eclipsing binaries you can observe and record data for with a pair of binoculars or the unaided eye. If the star has an amplitude of at least 0.5 magnitudes in V and it’s average brightness is 8th magnitude or brighter, chances are only you and a handful of others are observing it.
There are some stars that have been observed for a hundred years or more, and hundreds that have been regularly observed (almost exclusively by visual observers) for many decades. It is this long-term coverage that is of particular value and interest to researchers.
As an example, for any variable with a long-term well observed light curve the scientific values of visual observing come from (a) the long time span, (b) the statistical similarity of errors from visual observers, and (c) the bandpass similarity of human vision across a wide population of observers.
For point (a), long time spans can do at least three valuable things: build up signal-to-noise in the signal domain where there are weak signals less than 0.5 magnitudes; increase frequency precision where periods are stable over the long-term; and uncover long-term changes in behavior.
For point (b), signal processing in the presence of noise is something researchers deal with all the time, so the fact that binned visual observations may have an rms scatter of 0.1-0.3 is not a big deal.
What is much more important is that for a large population of observers, the errors are normally distributed. So when we have a light curve with dozens or hundreds of observers, that's actually a plus, because it makes it more likely that analysis techniques designed for data with normally distributed errors are going to be appropriate.
For point (c), this is really important, because with visual observers, the bandpass under observation may be somewhat fuzzy, but at least it's nearly *the same bandpass* across a sizable population of observers.
In order to continue this long timeline of visual observations into the indefinite future, the AAVSO encourages you observe these Legacy Stars as part of your visual observing program.
Legacy Cataclysmic Variables 
The Faint Realm
For the time being, there is also a gap in coverage of stars fainter than magnitude 13. The survey most cited as competing with visual variable star observers, ASAS, covers stars from 8th magnitude to approximately 13th magnitude. Observations of Mira variables with minima fainter than 13th magnitude and monitoring cataclysmic variables whose outburst maxima is fainter than 13th magnitude have the potential to be scientifically valuable by filling a gap in the current all sky survey coverage.
There are some variables known to undergo unpredictable, dramatic changes that should be monitored for activity every night. Among these are the R CrB type stars and Recurrent Novae. There are only a couple dozen of these stars in the sky, so they are rare stars that have rare fading episodes or outbursts. More often than not, diligent amateur observers are the first to detect these events.
New objects appear to come and go, and following these transient events is usually very exciting and interesting. Galactic novae are the obvious targets. Many of these rise to brighter then 8th magnitude at maximum so they are too bright for surveys, ground based telescopes, space telescopes, even your typical CCD observer to observe. Occasionally, one will reach naked eye visibility. These important novae observations at maximum light are nearly always visual data.
Professional astronomers regularly ask AAVSO observers to observe particular ‘campaign stars’ to correlate data to be taken with space based instruments or large ground based telescopes. Sometimes all that is needed are a few reliable visual observations to verify that a CV is in quiescence and pointing a multi-million dollar space telescope at it won’t destroy the detector. See the AAVSO Observing Campaign page  for a current list.
Away From the Stare of Surveys
The simplest way to supply data that the surveys can’t is to look where they are not looking.
Low on the Horizon
Survey telescopes tend to avoid the regions of the sky that are setting in the west as the Sun goes down, and they avoid the areas just emerging from conjunction with the Sun in the eastern morning sky. These observations are also important because they help to fill in the seasonal gaps in data for these objects.
Survey telescopes tend to avoid the circumpolar regions also, due to the inconvenience and challenges of pointing toward the celestial poles. Additionally, only half of all ground based surveys at any given time can observe either polar region. Telescopes in the southern hemisphere will never observe the north celestial region and surveys in the north cannot observe the south celestial pole.
Many survey telescopes completely avoid crowded Milky Way regions preferring to stare out to the vast emptiness of space between galaxies. Others have difficulty obtaining quality photometric results in crowded fields due to pixel scale, so even if they are looking the data aren’t necessarily science quality. Your favorite variables in the heart of the Milky Way will remain viable objects for visual observers for a long time to come.
As you can see, there are still thousands of stars visual observers can observe and still contribute to science. So get out there and observe some variable stars!