I don't know where to even start on getting my CRT TV, for example, to accept an RGB signal. It has all the major connections mentioned above, but I am still unsure what to do from there. I am happy as can be with S-Video out for my Neo Geo, but I would love to see my Genesis output RGB.
You'll notice the biggest difference on a Mega Drive, because as mentioned they are renown for having horrible composite output.
The first thing you need to do is determine whether your TV accepts an RGB signal. Not all TV's do, even ones with scart inputs. Some TV's have scart inputs but only accept a composite video signal, though this is rare.
So, does your TV have a scart input? What brand is it and what's its model number?
If your TV does have an RGB scart input, you will need to get an RGB scart cable to suit your Mega Drive. This is a link to a reputable eBay seller who sells high quality RGB cables (pcenginesales):
http://myworld.ebay.com.au/pcenginesales&ssPageName=STRK:MEFSX:SELLERID <- She's a member of these forums too. Find a cable to suit your console, make sure it is RGB.
Then all you have to do is plug it in and you're away, as simple as that. Most TV's will auto detect the signal and switch to the appropriate AV mode. If not, there will be a setting to do so somewhere.
If your TV doesn't have a scart input, but does have component you can use a converter such as the CSY-2100 or for a cheaper equivalent the CVS-287. These devices take an RGB scart signal and convert it to component. This is the next best thing to an RGB scart connection. I have one myself but I much prefer a straight scart connection. They are prone to some image distortion, they're not perfect.
Another (more expensive) option for the Mega Drive is the XMD-3 from Micomsoft. The XMD-3 converts the Mega Drive's signal in to pure analogue RGB, it has S-Video out as well as an 8 pin + 15 pin analogue RGB connection.