I have a Netbook with a 1.6 GHz Atom - an Acer Aspire One AOA150 with 1.5 GB RAM and XP Home. Doom 1 is playable, I get about 6 realticks per 5 gameticks in the standard benchmarks, with screen size one tick below full so the status bar remains visible but there is no border, with music and sound enabled. For anything much beyond that (Quake 1, for example) it is too slow.

I have an Acer Aspire Revo AR3610 nettop that runs Duke Nukem 3D fine at 320x200 in DOSBox, but it may be due to the nVidia ION chipset.

I've got an Acer Aspire One A150 (Atom N270 @1.6 GHz).
Duke3D ist playable even at SVGA resolution (800x600). There are some lags, but it's still alright. You can play anything up to Warcraft II or Crusader without any problems.
For glide games use ykhwong's build, Tomb Raider works perfectly (IIRC I had to fiddle about with different glide wrappers to resolve graphical glitches though).

It's definitely powerful enough for games like Syndicate, XCom 1 u. 2, Albion, Doom etc.

I know this thread is a bit old, but I just wanted to confirm that a 1.6g Atom ASUS Netbook is enough machine to run Dosbox. I'm running early 1990's games like Doom II, Commander Keen, Electro Man with soundblaster sound or even General MIDI music. No problem in a factor 2 window or fullscreen, even with advanced graphic interpolating. A factor 3 window goes off the bottom of the screen on an 8.9" lcd. There's a place on the web selling ASUS refurbs for two hundred bucks or less; what a way to get a mini dos game machine for cheap!

The real demanding games started around 1993 with the introduction of DOS4GW. Probly any game before 1995 would work fine on the atom.