Pros:
Rocket grab + tower + Power Fist = success in lane
Farmers like none other
High Survivability if you build a little tanky with tons of mana
AP stacks 100% with ult Active and can dish out some serious nuking power
Cons:
Mana efficiency is low before Tears of The Goddess in early game
Being scrubby with your grab will make you a hated champ in your team
Needs to be in a clear battle field or really lucky/skillful to land a good grab
If doing well you will be hated on by the other team :D

The only thing you can contribute to your team, which is the most important role is the Rocket Grab. This means not getting kills (sometimes) but securing kills :D. This is a role normally Karthus would take but only in the range of your grab.

So lets say Anivia is behind her wall (again)and the are no minions and there is a fairly low health enemy champ on the other side. Grab him and he dies with THE POWER OF FRIENDSHIP/TEAM WORK!

Generic Spell Caster Runes. Yeah that just how he rolls. But, Having the gradual cool down reduction will benefit you by not having to buy another cool down reduction item.

Spell pen for ult
Mana regen for spells
Cooldown for everything because low cool down for grab and your ult( 20 sec cool down ult 0.o)

Generic Caster. Good hands in case of getting targeted. Clarity for the Nidalee that you are so great with, and flash for getting away in clutch moments.

ULT + ABILITY POWER = INSTANT CREEP WAVE DEMOLITION

Teleport can be used for easy backs can be interchanged with the 2 posted
Ghost can be used instead of flash but not as efficient
Clairvoyance is great for spotting ganks and can save you a death

Anything else is not really worth it

First off is your q, You want this simply for the utility. Bring the enemies to you. and max it out when in your last few levels.

E: is required at lvl 2 because it will allow another second of attacks for your tower and your ganking teammates

W: is great for adding stacks to your Tears and getting to your tower with amazing speed.
With Nidalee, your attack speed will be about 1.001 at lvl 4 so demolishing an enemy tower is easy.

max E and W same time for a balance of faster attack speed and knock ups

Max your ult whenever possible

Max Q last

I have seen some ultimate fails when coming to enemy initiations because they focus on 1 guy or in this scenario your laning buddy Nidalee :D. Lets say Xin has initiated like always and got your nid in a fix. You are in the bush waiting for an opening when this happens. they are almost at your tower and Xin is ready to kill her.
Do you
a. run with her
b. grab xin and pull him into the push at a safe distance so nid can heal and live
or
c. run with her and Power Fist Xi for a sec and can use his dash to kill Nid.

The answer is b
this allows for a 1v1 situation of death to your ally, to become a 1v0 and now anyone can live not just Nidalee
You are more or less some type of savior.
But this requires massive amounts of skill and timing and a hint of luck for effectiveness so practice with Ezreal for the proper training.

Your team initiated in a jungle battle :DDDDDDDD (Blitz's fav) and trundle being well, trundle set up a Pillar of Filth and Ashe is "escaping". Grab her back and kill secured.

Nidalee: Happiness in a lane
Lux: Perfect for the grab
Maokai: Root for Grab
Udyr: Ganks like a boss and stuns for that perfect grab
Morgana: snare and grab for max effectiveness
SWAIN!!!!!!: This guy is a boss. Not just 1 skill snare but a group snare. None may escape from the Raven's Talons. I think it is a 1.5 snare which is more than enough for a good grab. LAZER BIRD!!!. So slow its amazing, not perfect but effective.
Any fear users is okay but they do move around a bit and can be a little troublesome for the grab.
Any stun/knock up user is ideal

So Lets review. Excellent farmer and nuker, but can survive in a huge fight for longer because of shield. Balance defense stats and mana for max survivability.

When a friend has baked you a pie and you ask what flavor, stop yourself because its going to be pie flavored. (This is plagerized from ASDF Movie 2 http://www.youtube.com/watch?v=tKB4h9gvmm0)