I have a Dell Inspiron XPS Gen 2 laptop that has a PCI-Express based 7800GTX card with 256MB of memory, 2GB of system RAM, and a 2.1GHz Pentium M running Windows XP SP3. Alas, the last big game I tried to play on it was Call of Duty 4: Modern Warfare. Ran pretty well at 720p on a 1920x1200 LCD screen. I also ran Final Fantasy XI on it with all the bells and whistles turned on, but I know that's not impressive game was released in 2003). I think it'll play Portal, though. Never tried Portal 2 or Half-Life 2 on it yet, though I possibly could. Plays Doom 3 pretty well. I'm sure it'll run Elder Scrolls IV: Oblivion as well, as I had it installed for a short while when I first bought it. Never tried Skyrim, the Tomb raiders, etc. I'm just brainstorming the games I have that I could try on it. The Witcher 1 would run with no issues. 2 & 3 might be a different story.

Well, as for Portal i'm sure it will run because i've tried Portal 1 and 2, and even Left4Dead on a Pentium 4 1.7Ghz (sk423) and a Geforce 6800, and it did....drag.
The newest game i ever played was UT3 on my very Geforce 7800GS until i retired it in 2008 or 2009. But all those games are way too "old".

In a modern computer, say a i5 or i7 with a Geforce 7950GX2, would any modern game run on that card or is it complety cut off the race because of a lack of a newer directx support?

Don't know. Would be fun trying, though, even if the FPS are garbage.

Tested pretty much all of this a while back, 3.2GHz Northwood with 4GB of DDR-400 and a 7600GS 512MB AGP, WinXPProSP3. HL2 and Portal "runs" with everything set to minimum or near minimum settings, gets pretty decently playable framerates too. Oblivion runs alright, again, provided you manage your expectations. Not quite minimal settings there, but not too far above them. Skyrim... runs, though at its minimum settings I was getting about 20FPS, so the proper term here is more "brisk jog". In Skyrim's case I'm almost certain the CPU was holding me back, considering its posted minimum was a dual-core @ 2GHz. Didn't have The Witcher 1 or 2 at the time but based on how they run on my T450, I'd say 1 would run with some sacrifices in graphical settings and 2, while it would maybe start up, would be a >1FPS affair. In the menus. Rather shocking how a game released in the same year as Skyrim can be so much more intensive. 3, as I understand it, is full on D3D11 so it won't run on the 7 series, and won't run on WinXP. If it could though I'd say it would be just as bad as 2 if not much worse.

So i guess DirectX compatibility "killed" the Geforce 7 generation chance of running any of todays games at all. Either way i've always saw the Geforce 7 as a glorified Geforce 6 that came out in 2004. A bit like the Geforce 4Ti was also a glorified Geforce 3 that couldn't run any games at all a few years later also due to DirectX incompatibilities.

I liked Crysis and Modern Warfare 4 on my 7800GTX 256MB

I've tried a 7600GS AGP in a few games with a P4 CPU, the most demanding were Skyrim and Fallout 3. Skyrim was definitely slow, but if I was living by the standards I had in the 90s I would have played it that way.
Fallout 3 was pleasantly playable on low settings IMO except for combat. That's unfortunately a problem with the design of F3 - it's framerate requirements are all over the place depending on the situation and it doesn't auto adjust details to compensate. I wonder how much the CPU might be a factor in combat though, with all the AI activity that's taking place.

In those games I found that the main limitation is the shader performance. They respond more to overclocking the GPU clock than they do to the RAM clock. I assume this is the typical bottleneck for later games on GF7 cards. Surely the P4 CPU was also a limitation though.
The 7600GS works well with FlatOut and FlatOut 2, but those games aren't as recent either.

I haven't tried Mount&Blade/Warband, but from searching it looks like it will work.

Unlike my older cards (not sure where the cutoff is), the 7600GS is compatible with Faster Than Light and Terraria. I haven't tried any other modern indie titles with it. Many of those aren't very demanding but they can have the issue of requiring modern API versions. I would guess the GF7 cards generally have a good shot at working with indie stuff from a few years ago like the above titles, and maybe even recent titles (I haven't looked into it much).

I just looked up Darkest Dungeon and it looks like sadly that won't work. It's written for OpenGL 3.2 which according to an nVidia driver note appears to require a Geforce 8 series, which conveniently isn't available in AGP.
I haven't bought DD yet but it's the type of game I was hoping to be able to fire up on my older machines, not just the modern one. With WinXP support and syncing via the Steam cloud, it almost achieves that, so the late OpenGL version requirement is a bummer.

War Thunder should still run, at least air battles.

The lack of raw performance and the meager 256mb of vram made sure this generation of hardware would struggle in anything newer than 2009-2011 ish games but the general rule is if it runs on the PS3 it will run on the pc port. There comes a point where one accepts that time has moved on and plays the newer games on another rig.

Fast XP rigs will be a thing someday with much faster cards.

I'm sure some indie games will run fine; more modern games will struggle due to the 256MB limit. Grim Fandango remastered, perhaps?

My last big upgrade back in 2005 started with dual 7600GTs in SLI to run Oblivion. With one card it was very slow, but two was pretty good.

They don't even have enough memory for Aero and a load of apps these days.

Upgrading to an 8800GTX made a small difference in performance..