Photometer vs. CCD-camera The Wikipedia article on photometry says that 


  These have largely been replaced with CCD cameras that can simultaneously image multiple objects, although photoelectric photometers are still used in special situations, such as where fine time resolution is required.


How much the research community is using photometers today? I looked up the prices of some photometers from here. The device, filters, etc. can cost nearly $2500. One could get a good CCD camera with that price.

What are some applications where the good time resolution (apparently around 1 ms) would be needed? Are photometers equally useful with small telescopes (e.g. 8-inch) as CCDs?
You have correctly identified a niche for photometers. Another point in their favour used to be that they were much more sensitive in the U-band than CCDs, but I think that newer CCDs can almost match or surpass the U-band response of photometers.

CCDs take quite a time to readout. The faster you read them out, generally speaking, the higher the readout noise. By comparison, the output from photometers can be very fast indeed with little impact on the noise characteristics. One of the beauties of photometers is also that they give you an instant readout of how many photons have been detected, requiring little analysis to provide real-time monitoring of signals.

However, things move on. So now there are CCD instruments that can work on extremely fast timescales. The primary example of this is a UK-built and operated instrument called ULTRACAM, which allows data-taking at 100 Hz and which uses a special "drift" mode of readout to achieve this.

Back to your main question - what are the scientific objectives of such instruments? On the link I provided above you will see a series of press releases that describe some of the science. These range from measuring the transits of Trans-Neptunian-Objects in front of background stars; examining detailed time series of flares on magnetic stars; investigating the eclipses caused by white dwarfs passing in front of companion stars; looking at the flickering output from accreting black holes; attempting to get phase resolved light curves of the optical emission from rapidly rotating pulsars and much more.

A rule of thumb is, that if you are able to obtain a time resolution $\Delta t$, then you are probing size scales of $\leq c \Delta t$, where $c$ is the speed of light. Thus if you can get a resolution of 0.01s, this corresponds to size scales of $\leq 3000$ km.

As to whether a photometer would be good on an 8-inch telescope, I'm not sure. When I was a student I used a photoelectric photometer on a small telescope to (i) study the scintillation of stars as a probe of conditions in the upper atmosphere - e.g. Stecklum (1985) - which has timescales of order $0.01-1$ seconds. (ii) To monitor "flare" stars with a time resolution of about a second in an effort to get real-time information so that spectra could be obtained at various points during a flare.