With Mac OS X Apple finally succeeded in releasing an operating system that (more than) matches the stability and simpliciy and beauty of System 6. However being build on an Unix base instead of the classic Macintosh operating system, it also is as far removed from system 6 as you can get. So, one can imagine that the compatibility of System 6 (and for that matter system 7) with OS X is rather limited...
Luckily they do share some compatibility...

Application and document compatibility
System 6 compatible programs that are not too old (like 128k and 512k era software) will run nicely in the classic environment within OS X. Docs created with these programs on a system 6 Mac will open effortlessly on a Mac running OS X. Otherwise you can convert docs that you created on your System 6 Mac using MacLink plus software, or by saving your docs as RTF (standard word processing format within OS X and supported by most system 6 compatible wp's), TIFF or PICT (standard macintosh picture formats already in use in the age of system 6), dbf (database) or anything Excel or tab delimited (spreadsheet formats)...

Exchanging disks between system 6 and OS X
OS X handles the System 6 HFS disc format fluently, so you can easily exchange docs between a System 6 and OS X on floppy. Keep in mind that most external USB floppy drives can only handle High Density disks.
Exchanging docs using a zip drive between System 6 and Mac OS X also works without any problems.
Same goes for cd's and other media with system 6 compatible drivers.

Sharing a network
OS X, starting with version 10.1 can connect to 'legacy' AppleShare servers. You can share servers running AppleShare 3, 4, 5 and 6.x between OS X and System 6 Mac using the 'connect to server' comand in the 'go' menu. It is also possible to connect your OS X Mac to a system 6 File server running AppleShare 2, or a clone of that software (download links are available here), only not via the go-menu. You have to have classic running and use the good old chooser to connect to a server that runs AppleShare 2 . If you don't have Apple Share fileserver software , you can setup a small fileserver with the inbuilt file sharing capabilities of system 7.x. When using System 7.1 you'll need to put the File Sharing Extension 7.6.2 (part of system 7.5.3) in the system folder in order to be able to hook up a Mac runnig OS X.

Connecting a System 6 Mac directly to Mac OS X 10.1
Appletalk If you want to connect your system 6 Mac directly to an OS X Mac using the appletalk protocol, you'll need to do two things:
1. You'll have to make your system 6 Mac compatible with the Appletalk Filesharing used by Mac OS X. In order to do this, you'll need to install Network Software installer 1.4.4 or 1.4.5 (AppleTalk (58.1.4), and then either install AppleShare for Workstations 3.5 (works best with multifinder turned on) or swap the AppleShare INIT of system 6 for the AppleShare extension of System 7.0.1. (this won't work with multifinder). BTW This setup will not only allow you to access OS X, but also Windows 2000 Service for Macintosh.
2. You will need to enable AppleShare via AppleTalk in Mac OS X 10.1.x Use the NetInfo Manager application and go to /config/AppleFileServer. Modify the attribute "use_appletalk" from 0 to 1. Restart file sharing in the System Preferences. Then you can use the SharePoints freeware application (linked is the latest 10.1 compatible version, check Versiontracker for the latest version) to share any directory, not only the public folders of the Mac OS X users, and you have converted Mac OS X to a full featured AppleShare server.
One last thing... Sharing a OS X hard disk with System 6 Macs works best when limiting the share to 2 Gig partitions. You are able to access larger partitions but you will run into problems when copying the same folder to the OS X hard disk more than once. Copying from a OS X hard disk partition larger than 2 Gig is no problem. System 6 cannot see the amount of freespace on a OS X hard disk partition larger than 2 gigabyte.
TCP/IP If you wanna share files over TCP/IP with an OS X Mac, you'll need to install mactcp on your System 6 Mac and use a FTP- or Telnet-program to connect your System 6 Mac directly to a Mac running OS X. You can read here how this done.

Sharing a printer
A LaserWriter that talks Postscript Level 2 can be shared by a System 6 and an OS X Mac on the same network. I have been able to share a LaserWriter IIg between an iMac running OS X and a floppy driven Plus running System 5.1. Because the LaserWriter is a postscript printer, files printed from your System 6 Plus will look just as nice as files printed with an OS X Mac.

You can also use OS X to share (new) printers that otherwise would not work with system 6. You can see how that can be done on this page