I'll try to sum up what I found at the wikia article about minions:
- 3 spawn in every wave
- 20 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
- 3 spawn in every wave
- 15 gold on Summoner's Rift
- 22 on Twisted Treeline
- +1 after the first wave
- +1 after every 5 minutes
- 1 spawn in every 3 waves (one every 2 waves after 35 minutes game-time)
- 40 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.
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 (22.214.171.124 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.
Edit 2: Katarina's passive no longer grants gold, instead it gives her a reset/cooldown reduction. Twisted Fate's passive no longer affects his allies