What effect do neutral buffs have in League of Legends?

Question

I know it is desired to get the blue buff for Ability Power (AP)-base champions and the red buff for Attack Damage (AD)-base champions and baron buff is good for everybody. I think blue buff at least increases your mana regeneration and red buff your health regeneration. So far I don't have any experience with maps (and therefore its buffs) other than Summoners Rift - I would like to know about these too.

What do the buffs affect in detail (preferring concrete numbers)?

Answer 1

NEW AND UPDATED ANSWER

INFO APPLIES TO CURRENT SEASON 3

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Summoners Rift buffs:

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Lizard (red) buff

Blessing of the Lizard Elder

• This unit's physical attacks slow the target's movement speed by (8/16/24)% (at levels 1/6/11) for melee attacks and (5/10/15)% for ranged attacks
• Deal (8 + Level * 2) true damage.

Golem (blue) buff

Crest of the Ancient Golem

• Regens 25 flat mana per 5 seconds
• Regens 1% mana (or energy) per second
• 20% cool-down reduction.
• Increases Max Energy (Cannot find source saying exact amount)

Both red and blue buffs last for 2:30 minutes without Runic Affinity and 3 minutes with it.

If slain, both buffs transfer to the killer.

Nashor buff

Exalted with Baron Nashor

• 40 ability power
• 40 attack damage
• 3% of your maximum health in health regeneration per 5 sec.
• 1% of your maximum mana in mana regeneration per 5 sec.

Lasts for 4 minutes with or without Runic Affinity.

If slain, the buff is lost but not transferred unlike the blue and red buffs.

Twisted Treeline buffs:

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Vilemaw (brownish) buff

Crest of Crushing Wrath

• Bonus health regeneration
• Bonus mana regeneration
• Increased attack speed
• 20% Cool-down reduction

(No source can be found with exact details, but this info was found on the wiki)

Lasts for 2:00 minutes or 2:24 with Runic Affinity.

If slain, buff is lost and not transferred (same as baron buff on Summoner's Rift).

Altar Buffs

One Altar

• +3 gold on unit kill

Two Altars

• +3 gold on unit kill
• +10% attack damage and ability power

Capturing an altar will give +80 gold to all players on the capturing team and vision of the altar

Buff is permanent as long as you own the altar.

Altars first open at the 3 minute mark and are locked for 90 seconds after being captured. Once unlocked the other team can capture and lock it for themselves.

Crystal Scar (Dominion) Buffs:

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Shrines

• When walking over shrines, the player gains a 30% movement buff.

These areas are neutral, so both teams can utilize them.

lasts 10 seconds or 12 with runic affinity

Health Relics

• "It seems to give you 15 + 1.25 x level % of your champion's max health (Pending Testing.)"
• Add 2 points to your personal score

These areas are neutral, so both teams can utilize them.

Greater Relic / Storm Shield

Increased champion model size. - A shield of 212.5 (+12.5 x level). - Passively detonate a lightning blast inflicting 90 (+10 x level) magic damage on champion auto attacks and damaging spells.

Mark of the Conqueror

This buff is granted to the first team to complete a "quest" on dominion.

• +10% to all damage types

50 seconds or 1 minute with Runic Affinity

Proving Grounds (ARAM) Buffs:

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(Same as Dominion Health Relic)

Health Relics

• On both maps, it seems to give you 15 + 1.25 x level % of your champion's max health (Pending Testing.)

These areas are neutral, so both teams can utilize them.

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FORMATTING TAKEN FROM @theorise

Answer 2

While @theorise explained the actual buffs, I want to touch briefly on your assumption that the golem buff (I'll call it blue for the sake of briefness) goes to AP champions and the lizard buff (henceforth, red) goes to AD champions.

Blue will increase your cooldown reduction, letting you use spells more often, and give you mana regen, so AD casters (Talon, Zed, Urgot etc.) will get full benefit from it. It's not something AP-specific. In fact some AD carries like Ezreal will also get full benefit in a poke comp (5 man team built around poking, think Jayce, Ezreal, Nidalee etc) since he can Mystic Shot more often and not run out of mana.

Red on the other hand only scales with your attack speed, and while that can scream AD carry, there's plenty of pure AP casters that scale with attack speed even more than AD carries (both ranged and melee, think Kayle, Teemo, Diana). Your typical AD carry will only really build a Phantom Dancer (or Blade of the Ruined King nowadays) for attack speed, where an AP Kayle will have a Nashor's Blade, Teemo will have Hurricane etc, getting even more out of that red buff.

I guess I should also mention blue can be good even on mana-less champions, like energy users (Akali!), or just plain resourceless (Riven!). The cooldown reduction is really noticeable.