I'm glad a thread like this popped up, because I've been trying to achieve this very thing for a while now. I've done quite a bit of research into it, but haven't found a 100% solution yet ... it's coming though.
The Mega Drive uses two soundchips to generate its sound. The primary chip is a Yamaha YM2612 which uses frequency modulation synthesis to produce its sounds. This was looked down upon during the time of the system, because the SNES' wavetable synthesis was thought of as superior (that's why the SNES sound was very sample based, orchestral, strings, etc. while the Mega Drive sound was synthy). Mega Drive music is an example of one of those technologies where people don't realize its full potential until it's long past its day. Anyways, it has 6 FM channels, and the last channel can be used either as a normal FM channel, or be loaded with PCM samples, primarily for drum sounds (or for that "SEGA!" splash screen). A channel could be panned either fully left, fully right, or center (which makes figuring that out rather easy).
The second soundchip is a Texas instruments SN76489 which basically had 3 square wave channels and 1 noise channel. It basically made very basic NES-type sounds.
These two cards were always used together to create the signature Sega music, so to recreate the Mega Drive sound, you will need 6 channels of FM synthesis, very 16-bit sounding drum samples, 3 square wave channels, and some NES noise (drum) samples.
The biggest challenge is the 6 FM channels, because, like I said, FM synthesis is way past its day. Apparently, the Yamaha YM2612 is VERY similar to the chips used in their famous DX line of synthesizers. I have found an FM synth VST instrument that actually takes Yamaha DX SysEx patches (here) and even copies the chip down to the four operators, and I have even heard rumors that there is a way to extract DX SysEx patches from the Mega Drive games themselves. Unfortunately, I have not found a way to do so. This seems like the last piece of the puzzle for me before I can accurately recreate these sounds.
The other requirements are not very hard to fullfill. Almost every soft synth can do square waves. 16-bit drum sounds are not very hard to create either, and NES noises ... well, we all have access to those in one way or another. ; )
In all, recreating the FM synthesis is the hardest part, and I'm almost all the way there! So, if everyone can look for a way to extract Yamaha DX SysEx patches from Mega Drive games, I think we will all be able to recreate Sega sounds.