You can convert CVBS (composite or single rca video) to RGB + sync, This is what your TV does to display a picture.
Doing it yourself will be a pain. The simplest way I can think of is to get an ADC that can handle CVBS (probably be easier to find one that inputs Y/C which is s-video or maybe one that does both CVBS and Y/C) and then you will need a DAC which outputs standard resolution RGB +sync. Like I said this would be one hell of a hardcore DIY project.
You could also use a NTSC demodulator like the TDA3566 or TDA3562 (both only accept Y/C input so if you use composite you will have to split that up first, or just hook the composite up to both and get a really bad picture) then you will also need to either use the composite line for sync, or Y (in the case of Y/C) for sync, or build a sync generator circuit.
Either way it will be a major PITA. Bottom line...use your TV.
Cheers,
-DT
*EDIT* If you meant component (YPrPb, which is three rca connectors) video to RGB this is easier, since this can be done with some op-amps because Pr and Pb are the difference to RGB when Y is subtracted. There was a thread about this a couple of weeks ago. Alternately you can also do this with an ADC and a DAC but that is somewhat more complicated to do at home, but possibly higher quality?