Exploration: If you can alert me, I can take you rafting. r5 Crash Shot harvests plenty of rafting. Otherwise, being elf-aligned or whatever can let you go into the desert and find Lost Elves - some of them are worth 1,000 exploration exp each.
Pets: Some are very decent, such as anything with a summon attack (dragons, Pegasus, scooter...) or anything particularly strong, like the griffon or Pegasus... you can see how these are mostly limited edition pets. Others will help in other ways, such as Herb Gnu and Cobra - poison attacks are based off the enemy's HP, so a properly placed poison strike can deal WAY more DPS than you'd ever be capable of achieving.
The main purpose for pets is storage though. You can rebirth pets into different animals, which will keep the skills they've gained but allow them to gain new skills - the Thunder Spaniel rebirthed into a pig, would still be a pig able to cast Thunder. Otherwise, rebirthing is RARELY useful for pets. They don't gain anything really.
Skill Resets: Only really useful if you play as a mage or alchemist and then realize this is a terrible start, and want to go melee or something. The skill training time isn't a big deal, especially with talents you gain skill exp faster than you gain AP, so don't even worry about that. You might also do some small trickery with this, like maxing Production Mastery, resetting it, then working on Refining, then getting Production back up - Refining is a unique skill because you're required to fail to level up. Otherwise, the reset is just in case you've started a skill path you don't like and want to try a different option.