How much gold do you receive for minion kills over the course of a game?

Question

How much gold do you receive for kills for each type of minion (range/melee/anti-turret) and how does this amount scale throughout the game? Also, if someone knows, how do I max money from creeps?

Answer

I'll try to sum up what I found at the wikia article about minions:

Meelee Minions

• 3 spawn in every wave
• 22 gold during the first wave on Summoner's Rift
• 29 on Twisted Treeline
• increases by 1 after the first wave
• +1 after every 5 minutes game-time passed

Caster Minions

• 3 spawn in every wave
• 16 gold on Summoner's Rift
• 22 on Twisted Treeline
• +1 after the first wave
• +1 after every 5 minutes

Siege Minions

• 1 spawn in every 3 waves (one every 2 waves after 20 minutes game-time)
• 27 gold during the first wave on Summoner's Rift
• 36 gold on Twisted Treeline
• +1 every 2-3 minutes

Increased Gold Income per Kill

There are a few champion abilities that increase the amount of Gold the caster gets when slaying a minion:

• Ashe's Hawkshot passively grants her 1/2/3/4/5 bonus gold per kill.
• Gangplank's Parrrley grants a bonus 4/5/6/7/8 gold if it lands the killing blow to an enemy unit.
• Katarina's Voracity grants her an extra 25 gold on each champion kill or assist.
• Twisted Fate's Loaded Dice grants him and his allies 2 bonus gold per kill.
• Smite grants 10 gold when used when enhanced by the mastery Summoner's Resolve Summoner's Resolve.
• In Dominion, Promote will cause the user to gain gold for each of the promoted minion's kills.

Summary

Like FallenAngelEyes said, you gain more gold the more times you manage to do the last-hit or killing blow on a minion. To get most out of a wave of minions just last hit as many as possible. If you have to decide between killing a melee minion and a caster minion and you can't get both, go for the melee as if gives more gold. Kill a siege minion whenever possible - they are worth the most.

Some numbers: Farming the whole first creep-wave gets you 114 gold, the 3rd wave sums up to 147 gold. Cleaning a whole wave after 30 minutes would give only 36 more gold. Therefore, it may be better to help your team and gain an assist than farming a whole creep-wave.
Another thing to know: the gold received from neutral monsters in the jungle and the dragon does not scale with game time, therefore killing these becomes less relevant over time.

Edit: With the Volibear Patch (1.0.0.130 released 11/29/2011) jungle monsters now give less rewards at the start of the game but scale over time - both difficulty to kill and gold/experience. I'll try to add some numbers as soon as I know them.

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