Aegis of the Legion: Unique Aura - Legion: Nearby allies gain 10 armor, 15 magic resist, and 10 health regeneration. +250 health, +20 armor, +20 magic resist. 2150 gold
Banner of Command: Unique Aura - Valor: Nearby allies gain 10 health regeneration and nearby allied minions deal 15% increased damage. +40 ability power, +30 armor, +10% cooldown reduction. Unique Active - Promote: Transforms a nearby siege minion to a more powerful unit. You gain all the gold this unit earns. 180 second cooldown. 2400 gold
Doran's Shield: +8 health regeneration, +5 armor, +100 health. Unique Passive: Blocks 6 damage from champion basic attacks. 475 gold
Eleisa's Miracle: +10 health regeneration, +15 mana regeneration. Unique Passive - Aid: Your Summoner Heal, Revive, and Clairvoyance cooldowns are reduced by 20%. Unique Passive - Eleisa's Blessing: If you gain 3 level with this item, you gain all the effects of this item permanently and this item is consumed. 1100 gold
Emblem of Valor: Unique aura: Nearby allied champions gain +7 health regeneration. +20 armor. 650 gold
Guardian's Horn: +12 health regeneration, +120 health. Unique Passive: Nearby enemy spell casts reduce the cooldown of Battle Cry by 1 second. Unique - Battle Cry: Gain 30% movement speed, 20 armor and 20 magic resistance for 3 seconds. 25 second cooldown. 1025 gold
Locket of the Iron Solari: +10 health regeneration. +300 health, +35 armor, +10% cooldown reduction. Unique Active: Shield yourself and nearby allies for 5 seconds, absorbing up to 50 (+10 per level) damage. 60 second cooldown. 1850 gold
Mikael's Crucible: +7 health regeneration, +40 magic resistance, +18 mana regeneration. Unique passive - Mana Font: Increases your mana regeneration by 1% per each percentage of mana you are missing, Unique Active: Removes all stuns, roots, taunts, fears, silences and slows on an ally champion and heals for 150 + 10% of the target's maximum health. (180 second cooldown) 2200 gold.
Philosopher's Stone: +7 health regeneration, +9 mana regeneration. Unique Passive - Transmute: Gain an additional 5 gold every 10 seconds. 700 gold
Ravenous Hydra: +15 health regeneration, +75 attack damage, +12% life steal. Passive: Damage dealt by this item works with life steal. UNIQUE Passive: Your attacks deal up to 60% of your Attack Damage to units around your target - decaying down to 20% near the edge. UNIQUE Active: Deals up to 100% of your Attack Damage to units around you - decaying down to 60% near the edge. 10 second cooldown. 3300 gold
Runic Bulwark: Unique Aura - Legion: Nearby allies gain 10 armor, 25 magic resist, and 10 health regeneration. +300 health, +20 armor, +30 magic resist. 2950 gold
Shurelya's Reverie: +10 health regeneration, +250 health, +10 mana regeneration. Unique Passive: +10% cooldown reduction. Unique Active: Nearby allied champions gain 40% movement speed for 3 seconds. 60 second cooldown. 2100 gold
Spirit of the Ancient Golem: +14 health regeneration, +500 health, +10% cooldown reduction, +7 mana regeneration. Unique Passive - Butcher: Damage dealt to monster increase by 25%. Unique Passive - Tenacity: The duration of stuns, slows, taunts, fears, silences, blinds, and immobilizes are reduced by 35%. 2000 gold
Spirit of the Elder Lizard: +14 health regeneration, +45 attack damage, +7 mana regeneration. Unique Passive - Butcher: Damage dealt to monster increase by 25%. Unique Passive - Incinerte: Basic attacks and non-periodic spell damage burn the target for 6-40 (based on level) true damage over 3 seconds. 2000 gold
Spirit Stone: +14 health regeneration, +7 mana regeneration. Unique Passive - Butcher: Damage dealt to monster increase by 20%. Unique Passive - Rend: Basic attacks deals 10 bonus true damage to monsters. 800 gold
Tiamat: +15 health regeneration, +40 attack damage. UNIQUE Passive: Your attacks deal up to 60% of your Attack Damage to units around your target - decaying down to 20% near the edge. UNIQUE Active: Deals up to 100% of your Attack Damage to units around you - decaying down to 60% near the edge. 10 second cooldown. 1900 gold
Warmog's Armor: UNIQUE Passive: Restores 1% of your maximum Health every 5 seconds.+1000 health. 2830 gold
Master Yi'sMeditate increases his health regeneration by 128.33 / 256.67 / 385 / 513.33 / 641.67 (+1.835 AP) for the duration.
Shen'sVorpal Blade marks its target for a duration; champions who damage the marked target gain 10 / 16.67 / 23.33 / 30 / 36.67 (+2.5% of Shen's maximum health) health regeneration during 3 seconds. Shen heals instantly for 1/3 of the total health regenerated instead if he kills a target with Vorpal Blade.
Healing reduction effects reduce the effectiveness of regeneration. Such effects do not stack, though they will refresh the duration. All such effects (except Crystal Scar's Aura) halve the effectiveness of healing, health regeneration, life steal, and spell vamp. See Healing for more information.
Health regeneration is one of the least efficient statistics to purchase, which the following will explain.
For example, if you divide the cost of the cheapest health regeneration item, Rejuvenation Bead, which is 180 gold, by the cost of health potions which are 35 gold each, you can buy 5 of them. If you multiply the number of health potions by the amount of health regained (5*150 = 750), and divide that amount of health regained by the health regeneration per second of Rejuvenation Bead (750/1 health regen per second = 750 seconds or 750/60 = 12.5 minutes), you find that health regeneration per second is a terrible stat to build for in most situations.
(The above isn't true, because you can simply buy a Rejuvenation Bead and sell it again later for a net loss of 54 gold, meaning a Rejuvenation Bead is more cost efficient than a Health Potion after holding the item for 4:00mins)
The only item that comes close to the 10 health regen per second of Health Potion per 35 gold (150 health regained/15 seconds to take effect/35 gold cost = .2857) is Warmog's Armor, which grants .2 health regen per second per 100 health, or for most champions, whose base health is ~3000 at lvl 18, is +6 health regen per second.
Compare this to health potion's 10 health regen per second, and Warmog's only becomes better than health potions when the champion buys Warmog's AND an extra 2000 health ((10-6) * (1/.2 health regeneration per second per 100 total health) = 4*5*100 = 2000 bonus health in addition to the starting value of a lvl18 champion + 1000 bonus health and health regen from warmog's.)