Virtual Console: The Wii's Virtual Console has, by far, the widest selection of Genesis games available on current-generation systems. 67 games are up for purchase in North America, including first-party titles, third-party games, and even a few imports (like Pulseman and Treasure's Alien Soldier. Unfortunately, at 800 Wii Points per game (900 for said imports), it's also the most expensive, so it's best used for purchasing single titles you can't get elsewhere -- like Pulseman and Alien Soldier, which you really should see about buying.
iPhone: Sega currently has four emulated Genesis games available for purchase through the App Store: Sonic the Hedgehog, Columns Deluxe (which also includes Puyo Puyo, aka Dr. Robotnik's Mean Bean Machine), Golden Axe, and Streets of Rage. All of them suffer from the obvious hardware issue of a complete lack of buttons.
Sega Genesis Collection: This budget-priced PS2 and PSP collection gives you access to 28 Genesis classics, including Sonics 1-2, all three Golden Axes, the Eccos, and even deep cuts like Kid Chameleon and Bonanza Bros. Other PS2-era collections, including Sonic Mega Collection and Sonic Gems Collection, offer even more Genesis and other retro Sega games, such as Sonic CD and Sonic the Fighters.
Sonic's Ultimate Genesis Collection: The Xbox 360/PlayStation 3 disc includes 40 Genesis games, representing almost everything from the PS2 collection plus several extras like Fatal Labyrinth, ESWAT, and, critically, the Streets of Rage series. This version also includes a filter for smoother graphics, and Achievements/Trophies, if you're into that sort of thing.
Gametap: The subscription-based retro gaming service offers a wide variety of Sega games, ranging from vintage arcade titles to even Dreamcast games, with plenty of Genesis games to play. You could be playing Shinobi III right now on your computer instead of reading this! Or, preferably, immediately after reading this.
Xbox Live Arcade: There are plenty of Genesis games available on Xbox Live Arcade, including (click links to add the trial version to your 360 download queue) Sonic the Hedgehog, Sonic 2, Sonic 3, Gunstar Heroes, Phantasy Star II, Comix Zone, Streets of Rage 2, Golden Axe, Ecco the Dolphin and Altered Beast, all of which can be had for 400 ($5) each. Nerd note: Technically, Golden Axe and Altered Beast are based on the arcade versions, not the Genesis versions, but since the Genesis was arcade perfect anyway, who's counting? It's also worth noting that the two-player XBLA versions all feature online play, something not found in Sonic's Ultimate Genesis Collection.