Do CD-R's play on your player? If no, why not?

Its not vodoo, it is design. The range of laser color used in DVD players will not read CD-Rs. If you burn music onto a CD-RW disk however, it should read (theheat sensitive ink dots are a different color. A few DVD players have two separate lasers and these are the only ones that read CD-Rs and DVDs. Within CD players, the reliability of CD-R reading is very variable. Often the error correction will simply declare a disk unreadable or part of a disk (causing skips). The basic design of the transport will determine how tolerant it is. The popular mid-fi Marantz units (modded into the Ah Tjobe as well are VERY poor at reading CD-Rs, for example). I use an ARCAM Alpha 7se as a transport because it reads almost all CD-Rs. Since manufacturers don't care about this per se, you really must try out a large assortment of CD-Rs (brands, music, data, etc.) on a unit before buying if this is important to you. DVD players are just not an option unless you burn everything yourself onto CD-RW disks which are more expensive than CD-Rs and somewhat less reliable in the long-term.

My Cal Icon plays cdr's just fine
but my older Nakamichi OMS-5 and Cal Aria do not
Seems newer machines can handle and track the poorer cut cdr's. Haven't tried any on my Toshiba dvd player

When burning a cdr you must close the session before it will play. Some software allows for the burning of the disk and leaving it open so that you can add more at a later time. I don't think cdrw's will play on anything except computers. probably due to the fact of not being closed. I play cdr's on my Theta Miles and a Magnavox cd650 (circa 1988) with no problem. Remember it must be burned as an audio disk. Audio cd's are no different than standard cd's. Make sure you don't use el cheapos. Color doesn't seem to be a big factor anymore either. Here's some good links for cdr info
http://cdrfaq.org/
and
http://www.cdmediaworld.com/hardware/cdrom/cd.shtml

FWIW, My Marantz CC-47 plays CD-Rs just fine. Never an issue with me. I've used both el-cheapo $0.10 USD blanks and expensive stuff without issue. Maybe I've just been lucky? The Marantz CC-47 is a 5 disc carousel, BTW.

And as others have mentioned, both DVD players will NOT play CD-R discs.