Since others are putting a top 3 I guess I will too:
1. Dreamcast
2. Sega Genesis
3. Super Nintendo
Why wasn't Sega Saturn involved in this discussion? There were several awesome games on that system.

1: Commodore 64
2: Amiga
3: Arcade

I feel that GOG should stay computer focused and therefore I suggest
1. Amiga
and
2. Commodore 64
and perhaps
3. Sega Dreamcast
as those are (like someone else said) really hard to get legally.
I really don't see the appeal in buying console games as I wouldn't be able to play them on a real system anyway. And while I generally enjoy playing SNES or Genesis games with an emulator, I really prefer to buy real cartridges and then download a ROM so my cartridge and my system can be safely stored away.

Amiga, definitely... and here are a hundred good reasons that barely scratch the surface: http://www.youtube.com/watch?v=hUoJBerFDsA
To be fair, most of the best of these are available for DOS too but I haven't seen many on GOG yet.
SNES would be cool too.

Wow, I'm so glad you took an interest in this suggestion. Having games from other platforms would be fantastic!
My choices:
1. Amiga
2. Commodore 64
3. Dreamcast
While there might be other good choices for the second and third spot, the Amiga is a clear favorite. Why? Well, the main reason is of course the excellent software library, with so many original and great games. The Amiga was the best gaming platform for a significant amount of time. The games are clearly old enough to have great nostalgic value, but they are also advanced enough to maintain great gameplay value today. A fair number of the games are also designed for mouse/keyboard control, which works well with the PC.
Kay

I'd go with Amiga first and foremost because of the commercial license for the system ROM's. You can't just find those legally elsewhere without paying. And paying usually means a lot more than here at GOG...
Second I'd say dreamcast as it is really hard to find any other way to play those games today and because it has some of the best games for any console... Shen-mue for example.
The third one is harder. Commodore 64 is pretty widely available so I think I'd go with Atari ST.

Definitely Amiga!!! And perhaps old MAC games starting from late 80's to mid 90's, running under OS 7.x, but Amiga is my top 1 choice!

Easy
1.Sega Dreamcast
2.Arcade
3.Super Nintendo
The first two because I would love to be able to get those games on a DD service, the third one does depend because I would say Super Nintendo because if I can get a copy of FF3/FFVI and chrono trigger on a DD service I would in a second but if not than Neo Geo becuase of the type of games., I know it's 4 answers but it's all good.

I can only pick 3 of these!!?! Okay...
- Amiga
- Dreamcast
- NeoGeo

Super Nintendo - Not even for the Nintendo games, which honestly I don't enjoy much anymore, but for the classic RPGs this system had. Shadowrun, Chrono Trigger, Secret of Mana... SquareEnix is on Steam, so they support digital distribution on PC... get it done!
Genesis - Same deal, really. Shadowrun there too!
Arcade - There are some great arcade games that never made it home, the top on my mind being The Simpsons beat-em-up game.

Not the toughest decision really:
1. Amiga
2. Commodore 64
3. Arcade

1. Amiga
2. Super Nintendo
3. Sega Dreamcast

1. Amiga

Definitely Amiga

Amiga
Super Nintendo
Rockstar :)