id Software (Todd Hollenshead specifically) have finally spoken and have revealed the official minimum requirements these are:

Minimum:
P4 1.5Ghz CPU (or equivalent).
384MB of RAM.
64MB graphics card (see below for chip details).
2GB of free hard drive space.

Lowest supported GPU is a Geforce 4 MX (worse than Geforce 3).
Supported cards:
GF 4 MX.
GF 3.
GF 4.
GF FX (and higher).
Radeon 8500s, 9000s and higher.

PC Gamer were the first to review they themselves recommend:
2Ghz CPU.
512MB RAM.
Radeon 9800.
5-channel sound card and speakers.

Mac Requirements:
Operating System: Mac OS X 10.3.8 or later
CPU Processor: PowerPC G4/G5 or later
CPU Speed: 1.5GHz or faster
Memory: 512 MB or higher
Hard Disk Space: 2.0GB free disk space
Video Card (ATI): Radeon 9600 or better
Video Card (NVIDIA): GeForce FX5200 or better
Video Memory (VRam): 64 MB
Media Required: DVD Drive

Recommended System Requirements
CPU Processor: PowerPC G5
CPU Speed: 2.0GHz or faster
Video RAM: 128MB

For historical purposes only:

From what John Carmack has said the minimum specification for running the basic DOOM 3 engine will be a:

1000Mhz Athlon/Pentium CPU.
256MB of RAM
GeForce 1 / Radeon 7xxx level of graphics card.

'Full impact' based on some estimates (not official):

1400Mhz Athlon / 1800Mhz Pentium 4 or higher speed CPU.
256MB of RAM + again quite dependant on how memory hungry your OS is.
GeForce 3 (original or Ti 500).

John Carmack long ago (QuakeCon 2001/2002?) said that the GF3/Xbox level of hardware would be full impact, in that dynamic lighting could be enabled and quality would be nearing the maximum, at 30fps and in relatively low resolution (we're talking 640x480).

Current (June/July 2003) high-end systems should be kicking ass:

Athlon XP 3200+ 3.06Ghz Pentium 4
512MB of RAM
Radeon 9800 Pro or GeForce 5900 Ultra

We've got benchmarks showing the kind of performance and we're talking 'good' performance from these kinds of systems, so hi-end today can manage DOOM ok with full on detail and 1024x768 resolution and higher.

Most people today (June/July 2003) have systems in-between 'full impact' and 'kick ass', as we don't have performance numbers you'll have to make a guess as to where your system would lie in-between what we have estimated 'full impact' to be and 'kick ass' systems.

In March 2004 some new requirements coming from a German magazine PCGames Hardware popped up these were totally false and id have denounced them as bogus, they were:

A video card with at least 128MB RAM and Pixel Shader 1.1 support is required for DOOM 3.
A 2.5GHz CPU should be enough for the stencil shadows and physics calculations.

We've got a lot of discussion going on in the forums regarding system requirements, so might be interesting to see what other people are 'speculating' in regards to higher up then just the official minimum hardware specifications.