I have always preferred the real systems, preferably relatively 'stock'/unmodified. but my reason for collecting has mainly been the fact that I had always wanted many of these systems as a child/teen but we just couldn't afford any of them.
I do have most of the emulators, and most of the TOSEC and 'Good' collections, but I much prefer the real things.
Comps:
VIC20 (+16k expansion)
Commodore 64 (x2, 1 boxed)
Commodore 64c
Commodore 128
Commodore 128D(cr)
1541 (x10)
1571 (x4)
1581 (x2)
Excelerator DD
SDuIEC
1750 512k expansion
Super1750 Clone 512k expansion
SwiftLink cart
Apple //e (x4) (+64k/80col for each)
Apple //gs (x3) (+1M card in each)
Mac Classic (4mb/40mb HD)
UniDisk 5.25" (x7)
Unidisk 3.5" (x3)
TI99/4a (x2, 1 boxed) (+FlashROM99 Command Module 'emulator')
Atari 600XL (+48k expansion)
Atari 800XL
Atari 520STm (+FDD & Color Monitor)
Coleco ADAM (boxed)
Amiga 1000 (+256k, +1M Phoenix board)
Amiga 500 (+512k)
Amiga 2000HD (030-33, 12MB, 700MB HD)
2x external floppies
CoCo3 (+2 FD controllers/drives)
Radio Shack TRS-80 Model 100 Portable Computer
Tandy 2500 RSX - Am386/25 (80387/33, 9mb, 450MB HD, 8GB HD, SVGA, SB, ZIP100, DVD, Ethernet, DOS622, WFW311)
Compaq Presario 4840 - PII/300 (192mb, 2x8GB HD, DVD, Win95sr2.1
Dell Dimension XPS T550 - PIII/550 (640mb, 2x20GB HD, DVD, Win98FE)
Samsung NoteMaster 486C/25 (TX486SLC-25, 4mb, 168mb HD, MonoVGA)
2x Seanix 486VLB systems I havent bothered to sort out yet
Consoles:
Atari 2600 Woody (light)
Atari 2600 Jr.
Atari 2600 Vader
Coleco Gemini
Sears Arcade II
Atari 7800
ColecoVision (x2)
Atari 2600 Expansion (x2, 1 boxed)
Steering Controller
Roller Contorller
Intellivision
Magnavox Odyssey2 (x2, 1 boxed)
Vectrex (+32in1 cart)
NES
SNES (x3) (+SuperGameBoy cart)
Nintendo 64 (x3) (1 w/mem upgrade)
GameCube (x3) (+2 GameBoy Players)
Sega Master System
Sega Genesis mk1 (boxed)
Sega Genesis mk2 (x3)
Sega CD add-on
Sega Saturn
Sega DreamCast
TurboGrafx16 (x2, +TurboED)
VTech Socrates
Sony PlayStation
Sony Playstation 2 (x3)
Panasonic 3DO
Yobo GN Twin (N8/Genesis)
Handhelds:
Gameboy
Gameboy Advance
Gameboy Advance SP
Nintendo DS
Sega Game Gear (boxed)
Sega Nomad
TurboExpress
NeoGeo Pocket Color
(several dozen older individual game HHs as well - no game and watch tho :/)
there's only a few things left on my 'wanted' list, managed to scratch one off getting that Mac Classic relatively cheap last month.
an Apple //c, a TS1000 (+16k), TRS80 (model I/II or III), a PET of some description, Atari 800. an IBM PS/2 Model 25/30
on the console side, an Emerson Arcadia 2001, Bally AstroCade and Fairchild Channel F, RCA Studio II, Atari 5200 - but I think the likelihood of finding these for a good price are slim.
for handhelds of course ANY Game and Watch, and the Mini Arcades (I have PacMan), the TomyTronic ones....just about anything from the 70s/early 80s really.
oh, and maybe an Atari Lynx.
(and, yes, I got a bit carried away listing all the *real* hardware I have managed to collect

)