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Imagine you have an scene with shutter speed 1/60, f/8 and ISO 200. Then you change the configuration to get an equivalent exposure: speed 1/120, f/5.6, ISO 200 (plus one stop in speed, minus one stop in aperture).
My question is, apart from the obvious changes in the depth of field due to the aperture change, and less blur for the speed change, would there be any effect in brightness, contrast, color or other? And what if the change is 3 or more stops?
In a theoretical sense, these things are perfectly interchangeable. See the second half of my answer to What is the "exposure triangle"? (after I get done ranting about the terminology). This is actually exactly the point of the "stops" system — you can think in terms of Exposure Value (measured in stops) and not need to worry about any complicated conversions between factors. So, in one sense, by definition, yes.
There are two wrinkles, though.
The first is that each of the adjustable factors can have effects beyond exposure and beyond the obvious ones that people learn first. That is, while aperture affects depth of field, it also affects other aspects of lens rendering, including aberrations (which are often worse wide open) and diffraction (which becomes a practical limit on sharpness as you stop down. Or, long shutter speed obviously increases the possibility of subject motion blur, but also might include camera shake blur — or of noise from warmer electronics.
The second is that the theoretical doesn't always match reality. This is particularly apparent in film, where longer exposures suffer from "reciprocity failure", which is basically defined as "whoops — stops stop being equivalent like they're expected to be". This particular problem is not the case with digital photography, but there are other areas where the imperfections of the real world may get in the way of theory, like the imprecision of measurements as Guffa mentions. And the nominal aperture and shutter speed scales don't actually perfectly halve/double every stop, but are generally within real-world tolerance. (Remember, the point is to make photographs, not scientific measurements, and in practice, these are rarely relevant.)
The intention is that the actual exposure should be exactly the same for equivalent exposure settings, but there are small deviations. There are also some other differences to the images other than the obvious (e.g. different depth of focus for different apertures).
Here are some differences that you may experience when choosing a different setting with the equivalent exposure:
Theoretically, the exposure would be exactly the same. In practice, the measurements are not exactly accurate. The f/8 might be f/7.9, the ISO 200 might be ISO 190. Those small differences keeps the exposure from being exactly the same.
However, the differences tend to be consistent, so if ISO 200 is actually ISO 190, then ISO 400 would be around ISO 380. That makes the difference in exposure between settings smaller than the actual inaccuracies of the measurements.
With different apertures you can get a focus shift, i.e. the focus plane can be at different places depending on the aperture. This is mostly only noticable for lenses with apertures f/1.4 and larger.
At small apertures, smaller than the diffraction limited aperture for a specific camera, the diffraction affects the image, which will make the images less sharp.
All kinds of distorsions, like perspective distorsion, vignetting, edge sharpness, general sharpness, will be more or less apparent at different apertures.
With very long exposure times (several minutes) the components in the camera heat up and can cause extra noise.
With different ISO settings you get different amount of noise.
With a digital camera, aside from increased noise (minimal at ISO 200) that comes with a longer exposure there would be no difference (given your exceptions).
With a conventional(?) film camera the effective film speed and/or color balance can change with long (greater than 1 second, depending on the film) exposures- see Reciprocity Failure for more detail.
Other than background blur (which you exclude), the main differences when you change aperture are:
