Can programs written in DOS or windows 98 be used on the computer
versions now available. I am not sure but I believe new computers
available now are xp only.
Can programs written in DOS or windows 98 be used on them?

programs written in Dos can be used on XP, just make sure it is written 4 winXp.
===========

MY view

Grub, a boot loader usually but not necessarily linked to Linux
distros, can be operated to allow a separate partition to be created
and booted on an XP computer. And, DOS is one such choice.

With map and hide and unhide commands, one can not only have more than
one Windows installation on the same HD, but they also need not
actually be in the first partition, the system is tricked into
thinking they are alone and on the first partition.

The problem, of course, is the need to reboot to run another system. 
And, of course, it is highly unlikely all your peripherals can be
operated in DOS, Some will depend upon what you wish to do.

The 'DOS Box' on XP is really an MSDOS emulator

I've found a couple of rather obscure bugs
- but have plenty of legacy code running on XP 

Much depends on what the Apps try to do, if they use undocumented
features then they will probably fail, similarly if they 'know' too
much about the hardware.

Windows Apps written under Win9x can also fail under XP, partly
because of 'security' and partly because Microsoft tightened up
checking for possible errors under the NT family.

http://sourceforge.net/projects/dosbox
DOSBox emulates a full x86 pc with sound and dos. It's main use is to
run old dosgames on platforms which don't have
dos(win2K/XP/linux/FreeBSD
http://sourceforge.net/projects/dbknitofrontend
dbfrontend is a windows tool to make the approach to the excellent
DOSBox project at dosbox.sourceforge.net more comfortable and to
manage DOSBox projects. (ie play the old DOS games