In Don't Starve: Reign of Giants, you can pick a Glommer Flower from Glommer's Statue during a Full Moon to make Glommer follow you.
What's the point? Is it for cuteness's sake, or is there any strategic advantage whatsoever?
As for Glommer's Goop:
Other than its use as fuel for a Fire (with a fuel value equivalent to Boards), it can be eaten, providing 40 health and around 9 hunger, but decreasing sanity by 50.
When killed, it drops Glommer's Wings:
Glommer's Wings are a nonperishable item dropped by Glommer used to craft the Old Bell. It is renewable as the player can obtain one each Full Moon by killing Glommer.
The Wings can also be used as fuel for fires or the Ice Flingomatic.
But note that killing Glommer will immediately summon Krampus.