PLACEHOLDER DESCRIPTION:
Take Battlemage in almost all situations.
Take Q build if you're on Shrines or possibly Tomb AND know exactly what you're doing

Put your mouse at the midpoint between you and an enemy hero. Press Impaling Blades then instantly press Primal Grasp.
Use Ravage to start your combo, catch up to a fleeing opponent, finish off a weakened enemy, escape to a minion wave, or provide healing through Siphoning Impact.
Use Maelstrom or Summon Ultralisk during teamfights.
Do not overextend. The closer you are to your target, the easier it is for them dodge your combo. Kerrigan is very vulnerable once her Assimilation shields are down. If you dive and miss your combo you're going to be instantly killed.
Be patient on your combo. Rushing it is the biggest chance of you missing.
Once you get Aggressive Defense, massacre minion waves to build up massive shields.

Updating this build now that Kerrigan is viable again. Gonna do a second sweep and clean up the guide in the next day or two.

Morales Patch:
With the recent Omegastorm nerf, I now recommend both Summon Ultralisk and Maelstrom. I still prefer Maelstrom but Summon Ultralisk is valuable if you need an extra body to block skillshots or need to zone a high priority target. Medic comes to mind.

At 20, Nexus Blades or Bolt of the Storm are now the best options. I actually recommend Nexus Blades unless you feel you are at great risk of getting picked off, such as from a Stitches' Hook.

Kerrigan has a lot of trouble getting value out of Bolt of the Storm, especially with its recent cooldown increase.

Cho'gall PTR:
I'm slightly worried about Kerrigan with the scaling changes. She's always struggled late. I still consider this build the best. We shall see how it works out, but unfortunately, I feel Kerrigan will become even more of a niche pick. But, don't let that discourage you, she is a very valuable hero to learn to play, especially on maps such as Haunted Mines.

I build entirely on one principle: What can I do to maximize my personal impact?
My build for the previous patch was built around entirely different talents.
I believe anyone can reach a very high level of skill. One of the best things about video games is that this is not hard to do. If you want to become a medical doctor, you're going to be spending years and be half a million dollars in debt by the end. Video games just take a few months.
That said, it can sometimes be useful to change your build around based on your current rating and skill. For example, you can swap out Maelstrom for Summon Ultralisk if you're still learning the proper time to dive. Torrasque is also very valuable if no one ever kills the egg, it basically gives you an 8 second ultimate cooldown.
Making substitutions based on your personal preference is also ok. If you really like Impaling Swarm at 7, go for it. You might even get more use out of it than Battle Momentum.
If you have more thoughts on the matter, I am always interested in discussing it.

"Try it, if it doesn't work for you, discard it."
- Ted Williams

Energizing Grasp returns too little mana.
Sharpened Blades gives too little damage. It is one extra auto attack every 12 seconds early game, half an auto attack late game.
Block is outclassed by Siphoning Impact.
Siphoning Impact will prevent as much damage as Block but also allows you to refill your health endlessly.

Fury of the Swarm doesn't increase your single target and the radius is small. This talent was only good when it had synergy with Battle Momentum.
Psionic Pulse is a weaker Burning Rage. It's still a good talent, but a few things prevent me from taking it; Not having 100% uptime, requiring a skill to activate, and having almost no synergy compared to Clean Kill.
Envenom should never be picked after its nerfs. Heroes that are forced to take it have all but vanished from the meta, such as Sylvanas.
Clean Kill provides the most burst damage out of this tier as well as free mana. It also allows you to use Siphoning Impact to completely refill your health anytime you kill a minion wave.

Assimilation Mastery provides you Rehgar's Feral Heart. You're a DPS, not a Healer. Conserve your mana instead. This seems to be a popular talent, and I'm not quite sure why. At level 7 it provides 3.54 health regeneration and 3.59 mana regeneration per second. At 20 this becomes 7.60 health and 4.85 mana. If you use Clean Kill on minion waves, like you should be doing, you will have no mana problems and will always be full health.
Impaling Swarm is weak. It has no synergy and dies to AoE. I only took it before the patch because there was nothing to use with Battle Momentum.
Adaptation has always been barely worth using. You should be using Ravage on enemies.
Battle Momentum ensures your Ult is always up. With Maelstrom's base 100 second cooldown, you will have teamfights when it is not up. Plus, a small cooldown reduction in your basic abilities during fights, which means more Assimilation shields and more life from Siphoning Impact.

Summon Ultralisk Solid, but with minor nerfs to this and major buffs to Maelstrom, I no longer use it.
MORALES PATCH: With the nerf to Omegastorm this is worth considering again.
Maelstrom has been granted a massive buff. 20% increase in damage across the board, 20 seconds off the cooldown, and it is now affected by Aggressive Defense for 20% bonus shields at 16 - from 20% to 40% - and 40% bonus shields with Omegastorm at 20 - from 40% to 80%.

Queen's Rush Too little effect and requires takedowns for full benefit. I like having talents that get me the takedown in the first place.
Double Strike Basic ability cooldowns are too long, and this talent does not deal enough damage. This is like Focused Attack, but at level 13 instead of level 4.
Eviscerate Solid talent, but the base range on Ravage is plenty long enough.
Lingering Essence Duration increase in combination with other talents now means stacking Assimilation shields before a teamfight is completely reasonable.

Blade Torrent Quality of Life talent at level 16. Get better at your combo instead.
Overdrive Not worth it. You already have mana problems, ignoring that, you're not increasing your damage by much. Kerrigan's strength is in her CC.
Essence for Essence Although I feel this is a buff over its current incarnation as Blood for Blood, it is outclassed by the Aggressive Defense buffs.
Aggressive Defense Now affects Ults. Massive synergy with previous talents.

Torrasque Very fun talent, but the mechanic is a little too unique for actual play.
Nexus Blades You're not relying on auto attacks and you don't need the slow. Too little benefit for a level 20 talent. MORALES PATCH: Expanding explanation. This is an ok talent on many heroes. Kerrigan just doesn't have the uptime to benefit from it and we're not taking any synergy related talents, such as Double Strike. Still worthy of consideration. After some tests, I found this talent gives you uptime. It helps ensure your cooldowns are always up with Battle Momentum and 20% AA damage is nothing to sneeze at.
Bolt of the Storm Nerfed and since Kerrigan has a leap built in, you will very rarely use this to engage. I would rather win the fight than be better at running away. MORALES PATCH: With the nerf to Omegastorm this is now a reasonable pick again. Bolt is always a solid talent, but I feel Kerrigan gets some of the least benefit ingame from it, which is OK, I still took it all the time. The problem is the cooldown nerf is massive. Before you could almost spam bolt. Now, with its ult level cooldown, you get significantly less use out of it.
Omegastorm Massive buffs to Maelstrom and Aggressive Defense also buff this talent. It stacks multiplicatively. With this and Aggressive Defense you are earning 80% of damage done by Maelstrom to heroes - and 40% to minions - as Assimilation shields. That is 150 health worth of shields per second per hero and 75 per minion or other object. MORALES PATCH: NERFED. Now does 60% instead of 80%.

IMPORTANT INFORMATION TL;DR: Both Ults are now good choices. Going for Bolt of the Storm or Nexus Blades is probably the best option at 20 now.

SLIGHTLY LESS IMPORTANT INFORMATION: Omegastorm has recently been nerfed. I recommend trying out Omegastorm, Bolt of the Storm, and Nexus Blades and seeing what you prefer. The choice is probably very situational now. If I had to pick only one, I see Bolt of the Storm now having the most average utility. However, Nexus Blades might also have some potential, I perhaps have underrated it.
I am also trying out Summon Ultralisk with this build. I like it quite alot.

The Morales patch has a bug fix for Kerrigan
- Kerrigan will no longer receive multiplicative bonuses to Shield generation after learning the Aggressive Defense and Omegastorm Talents.

I am currently very busy with college and have not been able to play at all the past few weeks. I'm going to test this and see if any modifications need to be made to the build. Expect an update today or tomorrow. Thank you.

I have played a few games on the PTR. I tried an Ultralisk build with more burst damage talents such as Impaling Swarm and Double Strike as well as this build with all three level 20 talents, plus a few builds with less drastic modifications.

I'm avoiding Bolt of the Storm on Kerrigan because I feel it is very at odds with her kit. I pick it up 100% of the time on a squishy mage such as Kael'thas but Kerrigan does not need a disengage. Once she uses her cooldowns she is not coming back into the fight anytime soon. It is better to soak up enemy damage with your shield. It is worth dying to win the fight for your team. That is not to say it is a bad talent, but with its recent cooldown increase, I feel you cannot force plays with it as much as just more damage.

I still feel underwhelmed by the build I used before the Kharazim patch and still recommend this build. The only thing that changes is possibly swapping out Omegastorm with Bolt of the Storm or Nexus Blades I would need to play more to confirm, which I cannot at this point in time. If you have comments, please post them.

I recommend trying out all three and seeing what you prefer.