Diablo – As a barbarian what are the [best] health regeneration options

No, since the Barbarian will be one of the main classes to choose when you want to play a "tanky" character, there are a lot of ways to get healed:

First, there's the templar. He has one ability that can flat out heal you, and one that can intercept enemies and heal the attacked player when you're at low health.

Second, there are item bonuses that grant life-leech, as a flat bonus or % of damage done, and also items that increase the amount of healing you receive from orbs.

Third, some skills of the Barbarian offer health restoration or regeneration. They are:

• Frenzy with Triumph Rune: Each enemy killed by frenzy restores 8% of your max health over 8 seconds
• Rend with Blood Lust Rune: Gain 9% of the damage done as health.
• Whirl Wind with Blood Funnel: Critical hits restore 1% of your max health.
• Ignore Pain with Ignorance is Bliss Rune: Gain 20% of all damage dealt back to life while the skill is active.
• Anciet Spear with Dread Spear Rune: Gain 60% of the damage inflicted back to life.
• Revenge: Heals 5% of your max life for each enemy struck.
• Revenge with Vengeance is Mine: Heals 8% of your max health per enemy struck.
• Furious Charge with Dreadnought Rune: Heals 8% of your max health per enemy struck.
• Overpower with Revel: Heals 8% of your max life for each enemy hit.
• Battle Rage with Swords of Ploughshares Rune: While the effect is active, critical hits have a 5% chance of making enemies drop health orbs.
• War Cry with Invigorate Rune: Increases your max life by 10% and also regenerates 310 Life per second while the effect is active.

As for "best", this is of course, situational, since you unlock some of these runes really late in the game (above level 50), but assuming that you have access to all of the runes above:

• Rend with Blood Lust Rune: If you have a lot of enemies around, 9% of damage done back to you should keep you at full health all the time, even for heavy hitting enemies.
• Ignore Pain: This skill in itself protects you from damage (65% for five seconds), so this should be the optimal skill to use if you get in dangerous low-health situations and need to heal back up. In combination with the skill above, you practically shouldn't die to anything but champions or named monsters, ever, and even they should have a hard time.
• Revenge with Vengeance is Mine Rune: 8% of your max health back is a lot, especially since (in my experience) Revenge seems to trigger quite a lot.
• Furious Charge with Dreadnought Rune: Not only does it heal you 8% per enemy hit, it also enables you to actually get out of dangerous situations should you ever happen to be surrounded (it happened to me and I tasted death :P )
• Overpower with Revel: This skill is instant and easy to use. It has a relatively low cooldown, but it can be lowered by 1 second if you strike a critical hit. This should prove especially useful later in the game, when you have some critical strike gear.

Those are 5 skills, you'll still need to bind something to your left mouse button so you can always use it. Frenzy is perfect here, since it's a great rage generator and also heals you with the Triumph Rune.

As a sidenote: I discourage the use of Ancient Spear with the Dread Spear rune: The damage it inflicts isn't a lot, at all, meaning the healing you'll receive is tiny. Plus, in higher difficulties, in situations where you need the healing, you'll want enemies away from you, not near you.