For many, the main value of the Dungeon Masters Guide (and possibly its greatest selling point) is its catalogue of magic items. Explicitly written as an aid for DMs to stock their dungeons with fantastical treasures, it is implicitly the equivalent of the old Sears Christmas Wishbook, that annual catalogue mailed to customers that included a section on every child's favorite subject: toys. Children traditionally pored through its pages, circling the toys they most desired in the hope that their parents, noticing the defacing of the catalogue, would recognize the meaning and pass the word to Santa Claus who would then magically fulfill their wish on Christmas Day. So it is with the Players Wishbook. Players read its pages as dreams of avarice dance in their heads, and they make lists of what they most desire for their characters.
These lists may take two different forms. The first, and oldest, merely consists of a note to oneself (the player) to seek information at the earliest opportunity about the possible existence and whereabouts of a desired magic item. If the player strongly envisions his or her character as wielding a rod of lordly might, then inquiries might be made the next time a sage is consulted. The sage might not know the answer, but he or she might know someone who does.
The second form of wish list consists not of personal reminders to the player, but requests submitted to the DM. The DM is supposed to decide which requests are reasonable and then work those items into a dungeon or encounter so that the player character will "coincidentally" stumble upon that item in the course of adventuring. Lo and behold! Your heart's desire was in the kobold's stash (or the ogre's bag, or the dragon's trove, etc.). This method was probably first suggested in an issue of Dragon in the 1980s (I seem to have faint memories of it), but it appears to have been institutionalized by post-1st edition gamers (and probably enshrined in the rules of some games).
Perhaps needless to say, I do not condone the second form of wish list. It comes too close to the actual granting of a wish. It clashes with immersion, it's lazy, and it feels too much like cheating. In the end, it's also a bit of a let-down. Oh, there's that robe of eyes I've always wanted. Let me just make a check mark on my (shopping) list. There. Next!
The first form of wish list is fine, but with one caveat: the player character should almost never be certain that such an item exists or has ever existed. The character may have heard of the magic item, but it might be nothing more than a folktale or the tall tale of an inebriated traveller. This enables the player character to make inquiries and remain in character because the magic item will at least be known in lore even if there is no such thing as an actual Apparatus of Kwalish in your fantasy campaign.