The Dell D630, E6400, or Lenovo T61 or T400 would do all of that just fine. In all of these cases, I recommend integrated graphics, just because on the D630 and T61, the discrete graphics has the potential to be unreliable, and on the T400, the discrete graphics is very weird and you will be permanently limited to Windows Vista or 7, in order to take full advantage of the hardware.
Worms Armageddon is a very old game and will require approximately no graphics horsepower at all, and Minecraft is a Java monstrosity that will almost certainly benefit more from having a reasonably nice 2GHz Core2Duo CPU than a particularly good graphics card. Plus, the drivers for the Intel GMA X3100 and X4500m graphics have updated in the past year or so, improving OpenGL performance on Windows a lot anyway.
If you still consider discrete graphics to be mandatory, the Dell E6400 is probably the way to go, and if Minecraft is really your only graphics-intensive application, this should be all the better, because the E6400 was available with OpenGL-focused Quadro graphics.
The EliteBook 6930p is of the same generation as the E6400 and the T400, as well.
http://www.geeks.com/details.asp?invtid=6930P-C2D226-MAR-R&cat=NBB
You can also go a generation or so back, this machine probably has the 945 chipset and it does say it has a discrete graphics card, but I can't imagine you'll like the graphics it has (GMA x3100 or 4500 would be better, on a machine with 965 or 4-series chipsets) but it'll take 4 gigs of ram (and use about "3.something" gigs of that) and will run all of the programs you want at a decent clip.
http://www.geeks.com/details.asp?invtid=6910P-C2D18-MAR-B&cat=NBB
One quick note on the E6400/Elite6930/T400, which are all based around the Core2 Penryn generation of processors. I only just stopped using mine (a ThinkPad T400) this past summer, and only for reasons totally unrelated to the performance of the computer. That machine still does everything I need/want on my home computer, and probably would for a while longer, but it started having an odd sound issue. (Sources online point to it having been in the software, one of my roommates is using it now, so I'll have to retrieve it and see if a reinstallation of Windows helps it at all, which will be nice because he uses it for wow, audio conferencing, and listening to podcasts in iTunes.) The machine has the discrete graphics option, but we run it with the GMA, because I think it also needs a new heat pad, or to be cleaned out of dust.
I don't know how long it'll be before desktop application software leaves computers from 2008-2010 (ish) behind, but right now, anything made in the past six to seven years does really fine, and with a solid state disk (which I have added to my T400), many tasks are indistinguishable between something of the Penryn generation from 2008/2009 and the Sandy Bridge generation from this year, even though Penryn to Sandy Bridge was in many cases an actual doubling of CPU performance, both integer and floating point.
I also have a ThinkPad T42p, a fairly high end Pentium M computer that shipped at about the same time the D610 did -- it does competently at a lot of the things my T400 does, but with only a gig and a half of ram and a quite old 128mb discrete graphics chip, it does fewer of them at once, and with a spinning disk (which would be exceedingly expensive to replace with a solid state, because it is IDE) it takes longer to launch applications and boot up. WoW runs, although this is nearing the older edge of playable -- GMA x4500 is significantly faster than the ATi FireGL T2 (Unsurprising, the T2 is about equivalent to a Radeon 9700/9800.) The main reason to go for something that old would be you're sure you're not going to be doing all that much at once (limiting the number of tabs you've got open) and favoring software that's slightly less compute-intense (The Zune media playback software, is fairly compute/graphics intense, and at its core, does the same stuff that bog-standard Windows Media Player, or Winamp does.) -- Also, the 15-inch 1600x1200 IPS display is really gorgeous, although a 14-incher would be far more portable. (Sidenote: That display is also available on the T60, and you can swap T61 motherboards into the T60 that has that display, but you'd end up spending a fair chunk of money to do that, since they're well-liked and you'd essentially have to buy the better part of two computers.)
"one more thing" to consider is that most of the machines (well, all of them) mentioned in this post have docking connectors, and at least the Dell and the Lenovo systems had docks available with PCI Express connectors in them. I don't have the information handy, but both of these vendors supported a few desktop level discrete graphics cards in the docking station, which may be something to look into if you just want a fast CPU today, and in a year or so want to upgrade the GPU so you can play a few more games. These would have to be games you can play offline, however, because the docks are not very mobile, they take up a huge amount of desk space and you would need a desktop monitor to display the output from a graphics card in the dock.
Hopefully some of this was even vaguely helpful.
