|In the following cd's refers to both cd's and dvd's (they are both cd's - compact disks).|
If it works fine with cd's burned on the same drive, and "pressed" (non-burned)cd's other than some video cd's, there's not much you can do. Video cd's (especially dvd's) may require that your drive supports the region code embedded on it - if you got the video cd's off the web, the region code may not be the same as the region code where you live, or not the same as the region code accepted by the drive - you can often change the region code in the drive's configuration, but often only a small number of times. You could check the manufacturer's web site for firmware updates for your model, but if there is no specific mention of the problems you are having it probably won't help to flash to a newer version.
Whether your burner can read cd's made in another burner is, unfortunately, quite variable - some models can read more of those, some less.
Media compatibility (brands, types of burnable cd's or dvd's)is also quite variable - some models are not too picky, some are (e.g. some Pioneer models). You can find information about that to some extent by reading reviews for the model you have, or by reading reviews beforehand for models you are considering buying.