Several people were amused with how aggressive I played Anub'Arak. I find him to be a unique hero in his ability to do large amounts of damage while healing himself and providing great crowd control. His ability to engage and disengage is unparalleled. I almost uniformly disagree with the statement that he's a weak hero. Although he could use some fixes to beetles as they're currently absolutely useless other than for tower fodder. A boost to health would be more than welcomed as well.
Knowing when and where to use underking is one of the biggest learning curves for Anub'Arak. This is a very aggressive build, but the key is knowing when to be aggressive and when to run away. Anub'Arak plays very much like a specialist. He works best when supported by Rehgar (lightning shield and heals) or Tassadar (additional shield).
The goal of this build is to maximize area of effect damage for laning and team fights. Once you hit level 4 you become an effective lane pusher and once you hit 13 you can provide some of the best sustainable lane push damage in the game(IMO) as most of the damage is passive AOE.
Once you reach level 16 it will be possible to nearly insta-kill most squishy heroes while also dealing large amounts of AOE damage to surrounding heroes. In addition to gaining life back from locust swarm and regeneration master.
More health = better
Anub'Arak's biggest weakness is his low health pool. Regeneration helps offset that a small bit. Your goal is to grab any health globe you can. If you're passing by a creep pack, kill the wizard and get the globe. Same goes for merc camps and bosses. Make sure you're near them when they die so you can get the globe. End game you'll usually end up with 40-50 hp/second. You'll start getting chunks of life back while your shield is up if you're not taking a large amount of damage. This is invaluable for a hero that needs to be played as a specialist.
A lot of guides will tell you to take underking, but with the nerf and then the buff to locust needles I find going damage is a much better pick. This allows you do deal splash damage. Makes laning more efficient and adds extra damage to clumped heroes.
I wish utricating spines did enough damage to give me reason to take it, but the speed boost from shed exoskeleton is invaluable. It helps you escape as Anub'Arak should very much be played in a poke and disengage style. It also allows you to chase down and put yourself into position to body block the enemy.
AOE damage + healing.
It's very easy to waste if you're in poor position and the enemy is not snared. Works wonderfully with heroes such as Jaina that have an AOE snare. It's not unheard of to end a fight with full life if you have plenty of targets for your locusts. It by no means makes you invulnerable, but if you're not being focused the enemy is making a huge mistake.
More AOE damage.
At this point you can mow through minion waves for globes and make quick work of buildings.
Blood For Blood
Damage + healing.
At this point there's not many heroes you can't absolutely destroy in a 1v1 situation if your cooldowns are up. If you coordinate with any other DPS there's absolutely no reason you can't insta-gib an enemy healer or dps.
This is really dependent on what you're going against and whether or not you're being focused.
For most encounters you'll want to go hive master for additional damage and healing.
If you're getting focused and finding it hard to survive you'll want to go hardened shield.