I want o build a new system that will run DOS 6.22 and maybe Windows 95.
The reason is I want to be able to run some old games I have without having
to use any sort of emulation.
 
My question is will DOS be able to run on an Intel Celeron using DDR memory?
Has anyone recently build a machine for this purpose?

DOS will run on anything. Is this even a serious question?

I guess you are right everything should be backwards compatible.

In this case, yes. Besides, Celeron and DDR are pretty old.

Not all MB chip sets support DOS. I believe the change for nvidia came with nforce 3 that did not support Win98 (DOS kernel) and older, only XP (NT OS2 kernel). I suppose the biggest problem would be driver support.

If all else fails. Try a Virtual Machine.

You need an old $50 computer. I wouldn't build.
Windows 95 only requires like 64mb Ram.
 
If you want to build, I would dual boot.

Dosbox works good and if you want to play games with out emulation.
You may need to get a system with A ISA sound card or a older pci sound blaster card but some dos games don't like pci sound.

For a long time, I played civilization-2.   The requirements were dos 5.0 or higher, or windows 95.   I kept installing this on every new os including vista 32 bit, where it ran without a problem.   I got stopped when I went to vista-64.  The reason was no support for 16 bit programs.
 
The net of this is that I think your games should run on any modern windows machine natively, just so long as it is a 32 bit os.   Can you test this out somewhere?

Don't forget, if you go the DOS route, you'll have to configure your config.sys and autoexec.bat file to load the drivers for all your equipment (ATAPI CD ROM, Sound Blaster 16 emulation, Modem/NIC if needed, etc).  Also, if you never had the chance to master memory managing in the 640Kb DOS world, good luck configuring the expanded/extended memory if you use such a setup.

Thank you all for pointing out the possible problems that might come up.
I think driver problems will be the biggest since I just want to use a motherboard with integrated graphics and sound. As for memory management I think something will come up from 20 years ago if I stare at the screen long enough.

Many of the new motherboards don't support operating systems older then XP. They will tell you it may run but they don't officially support it. Some of the hardware doesn't even have drivers for systems as old as 95.  
 
LOL on a side note, I actually have an unopened copy of Win95 been saving it for grins and giggles.

I've got at least 3 PI boxes buried out in garage that all have 95 on them.