This is homebuilt, Gigabyte 965P-S3 motherboard, 4 gig RAM, 2 CD/DVD burners: Plextor PX-755SA and Samsung Writemaster (can't find model number), both drives are SATA and  XP Pro.  
 
On this system with either Roxio or Nero I've made a couple of hundred CDRs with no coasters. Always ran at fastest speed, didn't matter how many other things were running on the machine.
 
Starting two days ago I've become a coaster factory, with either burner, either software, any speed (only tried down to 8x), with lots of other programs running or with NO other programs running. Doesn't matter.  
 
CDRs are Verbatim Datalife Plus injet printable -- I've used the brand before, but this is a new spindle. I tried non-printable Verbatim (all I have on hand) and that made a coaster also. Used these same CRS in a low end eMachines Vista machine and did 6 good ones in a row.
 
I've rebooted, I've made sure nothing else is running (system idle around 98% before starting). The error with the Plextor is "illegal request". the error with Samsung is "Cannot format medium. Incompatible medium - Illegal Request"
 
Any idea what's going on? Why all of a sudden both drives, or both pieces of software or all my CDRs don't work????
 
(and on a different topic, everytime I try a search here I get no results.... is there something wrong with the search function?)

The first thing is that the drives are bad. Not likely, but possible. It could also be the disks, but you said that they worked in a different computer. I say get a new burner for around $40 and try burning a new disk form there.

Maybe a update conflict. Do a restore back to when you know they worked.

There was a Windows update and it was just after this that this problem came up.....

There you go. Delete the update or do a system restore to before the update.

Otherwise burn at a lower speed, try a firmware update.
Check that the controller is using DMA in Device Manager.