I just bought the new stuff pack and I've been experimenting with the wishing well item. So far, the results I've gotten:

Wish for Child
Good:
- Limited time offer for free adoption (did not test if it worked)
- Guaranteed Try for Baby (did not test if it worked)
Bad:
- Evil child added to household
- Temporary infertility buff (did not test if it worked)

Wish for Romance
Good:
- Knowledge of ultimate pick-up line (tried this pick-up line on a complete stranger, their relationship immediately became lovebirds!)
Bad:
- A sim (of the opposite sex? idk if it's random) is created that has the "enemies with benefits" relationship with the sim who made the wish, not added to household
- Hopeless Romance buff - the well tells the sim to give up and gives them a sad buff. I think this might make all romance interactions fail.
- A ghost sim (again, I got opposite sex, not sure) is created that has the "girlfriend/boyfriend" relationship with the sim who made the wish - had "Mean" trait, not sure if that was random or not!

Wish for Youthful Vigor
- Add extra days to life cycle (I did this with a child Sim on the first day of their lifespan and it didn't actually change anything, it must turn back the clock when they've actually aged a bit)
-Energizing buff

Wish for Happiness
Bad:
- +99 Playful moodlet, "Can't Stop Smiling" that leads to death by laughter

What have you gotten?

Edit
Wish for Child
Good
-Child is added to the household with the genius trait
-Adopting cost 0 simoleons for a limited time

Wish for Romance
Good
-Sim of opposite sex is summoned with max romance and almost maxed friendship with boyfriend/girlfriend status.
-Given the interaction "Ultimate Pick-up Line" that drastically raises romance on the target sim

Wish for Youthful Vigor
Good
-Resets current life stage
Bad
-Sim loses all days of current life stage and force ages up.
-Sim is turned into a ghost.

Wish for Skill
Good
-Sim get one skill maxed out

Wish for Promotion
Good
-Sim is promoted by one level
-Sim's performance is maxed out but other requirements must still be met.
Bad
-Sim is demoted by one level.

Wish for Better Grades
Good
-Sim goes up by one grade.
Bad
-Sim goes down by one grade.

Wish for Wealth
Good
-A large sum of simoleons is given to the household
-Sim is given knowledge of another sims dark secret and can blackmail simoleons out of them. (can be used on any sims not part of their household)
Bad
-A moderately large sum of simoleons is taken away from the household

Wish for Happiness
Bad
-Sim is given the "Leaking Happiness" moodlet that gives 3+ sadness while they are around others but surrounding sims will be given a happiness moodlet when around that sim.

Wish for Life Ghost only
Good
-Sim is brought back to life.
-Sim is given one random ingredient to make ambrosia
Bad
-Fails and gives sim "Just A Ghost" moodlet with 2+ sadness

Wish for Better Grades
Good
-Grade goes up the next school day as long as other requirements are met

Are the results totally random, or are there certain requirements for specific results? Like if an angry Sim wishes for a child, do they always get an evil child? Or if your Sim is just so freaking happy when they make a wish, will it always turn out good? Etc etc?

It depends on what mood the wishing well is in. You can raise and lower its mood by throwing donations in it, $100 will make it go down usually, $1000 puts it in a neutral mood, and $5000 puts it in a good mood.

This is the well's neutral mood. It can give a good or bad result from your wish.


This is its bad mood, which pretty much guarantees you'll get a bad outcome.


Its happy mood looks slightly different from its neutral mood, albeit not by much. But it'll give you a good outcome.

Speaking of outcomes, there are 6? different outcomes for each wish. It will give you a moodlet with an 'x' (for bad outcomes) or a '+' (for good outcomes) at the bottom of it. One 'x' is slightly good/bad, two 'xx' is good/bad, and three 'xxx' is great/terrible.

I don't think it the faces really mean much. It seemed like even when it looked happy and I gave it a good offering it sometimes would still give me a bad outcome.

Also the neutral face looks like he has a wicked smile

It's the eyebrows, he's like, "HAAA!!"
I wouldn't make a wish when he looked at me like that, is all I'm saying.

SimsVIP has a complete lay out of all possible outcomes as well as other stuff about the pack

http://simsvip.com/sims-4-romantic-garden-guide/