Games: I have two copies of a couple of games, but there aren't many I have more than two of, particularly of releases for a single platform...
For instance, I have two copies of Star Wars: Rebel Assault for the PC and one copy for the Sega CD, but does that count as three considering that it's across two platforms?
I also have two copies of Micro Machines (for the Game Boy), plus Micro Machines 1&2: Twin Turbo for the Game Boy Color, which includes a colorized and slightly altered version of Micro Machines 1... (the link-cable multiplayer mode that was the reason I have two copies of the B&W game was removed) that could count, I guess, though Twin Turbo is GBC only so it kind of doesn't, considering that the GB and GBC sort of are different systems. But across platforms it is three.
I also technically have three copies of the base Disciples 2 campaign, once from m yoriginal boxed copy of Disciples 2, once from the second expansion, Disciples 2: Rise of the Elves, which was stand-alone and included the original campaign in the box, and once from the Disciples Gold Pack I got on Steam (for the first expansion, which I had not previously had) and gave me a third copy of the Disciples 2 campaign and a second copy of the Rise of the Elves one.
I also have three copies of Hydro Thunder, on N64, Dreamcast, and Gamecube (the latter in Midway Arcade Treasures 3).
Games I have two copies of for whatever reason, including two copies on one platform or copies of the same game on multiple platforms, include Battle Arena Toshinden (Game Boy, for link play); Super R.C. Pro-Am (Game Boy, for link play); Micro Machines 2 (in Twin Turbo on GBC for one copy and on the PC for the other copy); F-Zero (SNES) (I just have two working copies of the cart); Descent (PC) (once from the Interplay's 15th Anniversary Collection, once from the PC Gamer Classic Games Collection Vol. 1); Star Wars: TIE Fighter CD-ROM Collection / TIE Fighter '95, if you count them as the same game (really they're slightly different versions of the same game and are not entirely identical) (once, the DOS version, from Lucasarts Archives II; the other, the Win95 version, from Lucasarts Archives IV); Daytona USA (Sega Saturn) (once from the 3-in-1 collection, once included with a batch of games I got online.); Virtua Cop (Sega Saturn) (same reason as Daytona USA); Keith Courage in Alpha Zones (TurboGrafx-16) (one copy came with the first TG16 I got, another with the second...); Taking it To the Hoop (TG-16) (same as reason Keith Courage), Rally Championship (Network-Q RAC Rally Championship) (PC) (first copy I got in the box, the second copy came in a racing game collection I bought for the other titles); Hardball III (I have it for PC and Sega Genesis); Pac-Man (on Game Gear and in Namco Museum on the Xbox); Baldur's Gate II (PC) (got second copy because one disc of my first copy had failed); Starcraft (PC) (got second copy because the disc wouldn't install anymore and I needed to install the game on a new machine); Lodestar: The Legend of Tully Bodine (Sega CD) (got second copy because the first one had gotten scratched and wouldn't play properly anymore); Commander Keens 1-3 (first copy from registered shareware on floppy disk, second from Steam (that I bought in order to get CK5, which I hadn't had before); The Longest Journey (the first time on its own on 4 CDs, the second included in the Dreamfall Game of the Year Edition on a DVD); Driver (on PC and PSX); Extreme-G 2 (for PC and N64); Goemon's Great Adventure (N64) (have two working copies); Grandia (for Saturn (JP import) and PSX (US version)); Quest for Glory: So You Want To Be A Hero (VGA) (original standalone version and the version packed in the Quest for Glory: Collection Series box); King's Quest I (one from the PC Gamer Classic Game Collection, one from the King's Quest 10th Anniversary Collection); King's Quest V (one original boxed copy, one in the King's Quest 10th Anniversary Collection); The Legend of Zelda: A Link to the Past (SNES and GBA); Lemmings (PC) (one original boxed DOS copy, one Win95 port included in Lemmings Paintball); Lords of the Realm II (one original boxed copy, one copy included with the Lords Royal Collection); Lunar 1, sort of (I have the PSX SSSC version and the GBA Lunar Legend version); MDK (PC and PSX); MechWarrior 2 (PC Win95 and Saturn); Mega Man X (PC and SNES); Micro Machines V3 / 64 Turbo (GBC and N64); NBA Jam T.E. (GB and SNES); NHL '96 (SNES and Genesis); NiGHTS into Dreams... (Saturn) (once stand-alone before I had the system, then again with the Saturn I got); Outrun 2006: Coast 2 Coast (PC (Steam sale) and PS2); OutRun (SMS and Genesis); Panzer Dragoon (PC and Saturn); Re-Volt (N64 and Dreamcast); Samurai Shodown (GB and Genesis); San Francisco Rush: Extreme Racing / San Francisco Rush The Rock: Alcatraz Edition (N64 / Arcade port in Midway Arcade Treasures 3); Civilization II and both of its expansion packs, Conflicts in Civilization and Forgotten Worlds (original PC versions and (PC) Gold Multiplayer Edition, though GME does not have all of the content from the original versions (it is missing two thirds of the music) so the originals do still have value even with the GME); Star Wars: Rogue Squadron (PC and N64); Warcraft II: Tides of Darkness and expansion Beyond the Dark Portal (original versions and Battle.Net Edition); Wing Commander: The Secret Missions (PC and SNES)... and perhaps some I'm forgetting.
I sort of also have two copies of Betrayal at Krondor because I have one copy of the CD version and one copy of the freeware floppy disc version from the PC Gamer Classic Game Collection 1, if that counts.
As for controllers, the system I have the most controllers for is the PC. Not counting keyboards and mice, I have two working joysticks (a Microsoft Sidewinder 3D Pro and a MS Sidewinder Precision Pro), the latter with the USB adapter so I can use it on my newer computer which has no gameport; three working gameport gamepads, a Capcom PC Fighter 6, MS Sidewinder Gamepad, and a Gravis Gamepad (original kind); and two broken, nonfunctional gamepads I've held on to, a Gravis Xterminator and a Saitek P880.
For consoles the winner is the Gamecube, for which I have four working controllers and one broken one. The working ones are three official ones (black, orange, and purple), one working Mad Catz pad, and one broken official black pad.
There's a four way tie for the next spot. I have four controllers each for the SNES (two official, two no-name third party, with a Super Multitap to use them with), N64 (all official; two grey, two atomic purple), Sega Genesis (two official 6-button controllers, original style, one no-name third party 6-button controller, and 1 official 6-button turbo arcade stick, with both a EA 4-Way Play and Sega Team Tap (model 2) to use them with), and Sega Dreamcast (two official pads, one Interact, and one Mad Catz, all working).
For other consoles I have between one and three controllers.