Do you pluralize the singular possessions of / items or people associated with individual members of a plural group?

"Remind your wives" is the grammatically correct choice.

"Remind your wife" would imply the whole group shared a common wife. It's hard to imagine, so let's use some other term to understand the difference.

Remind your supervisor
Remind your supervisors

In the first case, the implication is the whole group has a common supervisor. In the second case, it implies that each individual has their own supervisor.

In this case, "remind your wives" is appropriate--assuming it's not one woman with many husbands.

It depends on how the item is shared (or not).

If you have 1 pizza with 8 slices, you and your 7 friends can share the single pizza. All 8 of you can eat the pizza.

If you have 1 cookie and 7 friends, that cookie will be very difficult to share among the 8 of you. But if you have 8 cookies, you and your friends can eat your multiple cookies. Each of you can individually eat a cookie.

If this comes up in the future, think about if it's something that multiple people can use/eat/drive/etc. at the same time.

I have to share an office with 2 coworkers, but we each have a desk of our own. Sometimes our secretary will say, "I put it on your desk" (my specific desk), and sometimes she will say, "I put it on your desks" (all three desks).

When addressing the group as a whole, you generally use the plural form. However, you can convert to the singular form by using each, as in

Each of you should remind your wife ...

Each man should remind his wife ...

The answer stated above as being the 'grammatical' choice sadly gives the impression that the alternative is wrong. It is not wrong (where no real scope for misinterpretation would ensue) to address the (common) individual within a group: 'Hold the protractor down with one hand.'

In this particular case, while 'Remind your wives' is certainly not wrong, 'Remind your wife' will almost certainly not add any confusion and would only be labelled incorrect by prescriptivists above a certain level. I can think of no 'grammatical rule' proscribing and am familiar with the acceptable usage of employing correctly formulated singular constructions when addressing more than one in a group (especially a largish or large group).

Dorgeloh and Wanner, in Syntactic Variation and Genre, state that

In [a] common strategy, speakers may use singular constructions [to simulate a 1-to-1 situation] despite a manifestly plural audience. Well-known instances of this are address forms such as Dear Reader in novels, editorials and so on. The pragmatic effect is quite clear: [t]he use of singular forms can be used to simulate closeness or intimacy, states which are usually absent from mass-medial communication. While 1-to-1 simulation is arguably easier where there is no physical co-presence of the addressees (for example, in the written medium or in TV or radio broadcasts), it may also occur in face-to-face situations, if the audience is sufficiently large[: t]hus sermons or speeches are situations in which ... 1-to-1 simulation may be used by the speaker.

The device of at times addressing the individual within the crowd was used in Hebrew by Moses (and his Boss), in Deuteronomy, as T A Lenchak, and doubtless other commentators, point out.