These must be addressed here because they are everywhere and they are so sneaky. You think the plant looks great but this one leaf curls oddly and BAM, there they are in enormous numbers.
As goes with fighting all of these pests, promoting a diverse garden with beneficial plants to attract insects that will predate these buggers is the most important part of gardening organically. Ladybugs and lacewings will eat some aphids but it might not easily solve your problem. In interior settings like greenhouses, predatory insects can be bought and released to good effect.
A heavy stream of water can do the trick of dislodging the guests and they usually struggle to climb back on the plant. Insecticidal soap can help keep them at bay. The best thing I’ve used was a homemade garlic and cayenne solution to keep them away.
Finally, plants that have too much nitrogen or are over fertilized (even organically) will be ripe targets for aphids. You want the plants to be healthy but not with overly succulent foliage.
Note: An interesting fact about ants is that they like to farm aphids for a milky excretion they like to eat. Going so far to protect their 'farm' from carnivorous insects like the ladybug.
Here’s a pretty classic recipe: http://www.vegetablegardener.com/item/7076/garlic-and-chile-insecticidal-soap-spray