Although I don't claim to be any great shakes in CIV3 you might not want to upgrade those units too reflexively. I have found several good uses for even the lowliest units.
1) Small groups, 3 or4, near an aggressively violated border can stop those pesky spearmen/settler teams without starting a war you might not want. This can free up more useful units.
2) Obsolete unit still suppress resistors as well as more modern units. Until this afternoon I didn't know this but if I read the dev forum correctly this seem to be.
3) A mass rush or helicopter drop can speedbump the response to an armor attack. Or landed/dropped on the opposite side of a enemy continent 2 or so turns before the real attack causes the enemy troops to get a 2 or 3 turn head start in the wrong direction. The poor spearmen get slaughtered but it still takes time.
4) The same mass rush of pillaging directly across roads/railroads can cut access to resources and luxuries that make enemy cities grumpy and unable to produce modern units at critical times.
5) I have been told, never did it myself, that if you have free passage in a neihboring civ you can disrupt his access to resources and movement of troops. I suspect you could passively help a third party reduce his power without risking anything. By any means if he declares war cheap units are less painful to loose seeing as that they will be deep inside enemy territory when the road bonuses disappear.
None of this means that obsolete unit shouldn't be upgraded just that they may not be, in some situations, as useless as they seem to be.