All of the standard open source utilities, like GCC, (X)Emacs, the X Window System, all the standard Unix utilities, TCP/IP (including SLIP and PPP), and all of the hundreds of programs that people have compiled or ported to it.
There is a DOS emulator, called DOSEMU. The latest stable release is 0.98.3. The FTP archives are at ftp://ftp.dosemu.org/dosemu The Web site is http://www.dosemu.org.
The emulator can run DOS itself and some (but not all) DOS applications. Be sure to look at the README file to determine which version you should get. Also, see the DOSEMU-HOWTO (slightly dated at this point—it doesn't cover the most recent version of the program), at ftp://metalab.unc.edu/pub/Linux/docs/HOWTO.
Work has been progressing on an emulator for Microsoft Windows binaries. ("Can Linux Run Microsoft Windows Programs?")
iBCS2 (Intel Binary Compatibility Standard) emulator code for SVR4 ELF and SVR3.2 COFF binaries can be included in the kernel as a compile-time option. There is information at ftp://tsx-11.mit.edu/pub/linux/BETA/ibcs2/README.
For more information see the INFO-SHEET, which is one of the HOWTO's ("Where Is the Documentation?" and "How To Port XXX to Linux.")
Some companies have commercial software available. They often announce their availability on comp.os.linux.announce— try searching the archives. ("Are the News Groups Archived Anywhere?")