You must also take into consideration that parts values, especially capacitors, change with age. As such, most old speakers need to be "re-capped" for best performance. Since caps have come a long way in the last 25 years or so, this can take some older designs that were basically quite good to start off with and actually improve upon the original design.
You also need to think about the internal wiring. Since copper does corrode and connections oxidize, you might as well replace the "antique" wiring ( that was probably low grade stuff anyhow ) with some fresh wiring also.
You might also want to look at the binding posts or terminals that most "antique" speakers use. Most of them were JUNK to start off with. They don't accept any "good" sized wire, were spaced too closely for use with "esoteric" speaker cables, used low grade metals, etc.... While i'm not going to say that you will hear a MASSIVE change in sound by upgrading these parts, i will say that it is possible that you could end up with a much more solid and lower resistance connection by doing so. Even those "cheezy" spring loaded terminals lose tension with time.
The inductors or "coils" used in many crossovers are typically pretty solid and can remain intact in most cases, but you can always find "better" if you really want to. Keep in mind that changing ANY internal component of the speaker WILL alter it's "voice" and the overall performance.
Sgmlaw's points about the spiders sagging with age is also very valid. One of my friends that owns a calibration lab and used to service audio gear for a living gave me a very good suggestion regarding this. What he used to do in order to prevent spider / foam sag and to help keep the voice coil centered was to rotate the driver a 1/4 turn every year or so. While this does involve pulling the screws and breaking the seal at the driver / cabinet junction, he felt that it was WELL worth it in terms of the measurable performance differences that resulted. Since he told me about this tweak, i have done it myself on several sets of speakers and will continue to do so.
As to buying speakers that have been "refoamed", be careful. Some folks don't do it right and the driver is off center. The voice coil drags, can overheat and even short out in severe cases. Keep in mind that the driver will need to be somewhat "broken in" again, as the suspension may need to stretch out slightly for best results. I've purchased speakers that had refoamed woofers in them that very little apparent bass. After some "heavy" listening sessions, the suspension has stretched enough to deliver both more and deeper bass than when i first purchased them. This is something that you might not expect to happen given that the same "old" spiders were still in the drivers. Sean