SimonG: No. They are still as awesome as they were back then.
Maybe Quake 3/Doom 3 could be considered "outdated". The rest is still great.
dyscode: Yes, actually the older games are more fun, since they have a much more creative leveldesign with lot's of secrets.
While D3 or Quake IV just rail you through nice corridors to shoot at things that jump out of closets. In that sense they seem quite dated. But the presentation is nice and I played other FPS games much, much worse.
D3, while linear, has some nice interactions & amazing music/atmosphere. I don't get why everyone seems to think linear game=bad game.
(Not saying you think/thought linear games are bad games.....I'm just speaking in general here.)
An aside: Many people state that Doom 1/2/Final are less linear than D3 and this is true, but the older games were a bit linear as well(With many levels requiring you to find colored keycards to progress further into/finish the levels.).
orcishgamer: Doom IIIs engine is still a powerhouse, imo, it looks pretty nice to me.
Have you ever tried the Ultimate Doom Doom3 mod? It adds even nicer looking graphics and(I think) some new weapons as well, such as a laser sighted pistol and a rail-gun mode for the plasma gun.