How do farmers keep bugs off of their organic crops, since they don't use pesticides and similar things?

Because they DO use pesticides......http://www.ocf.berkeley.edu/~lhom/organictext.html

The answer is some organic farmers DON'T keep the bugs off- and their crop yield is, on average, 20% smaller as a result (one of the reasons they have to charge more to stay in business).

Non-synthetic pesticides are still allowed-- but the line between "synthetic" and "natural" is blurry.

And while plenty of people are scared of the chemical pesticides "regular" farmers use, studies have shown that these chemicals are not really any more dangerous than the "natural" pesticides that plants produce themselves to ward off bugs. Here's the article, with study referenced to prove it: http://tierneylab.blogs.nytimes.com/2007/06/06/synthetic-v-natural-pesticides/

In other words, "organic" is mostly a scam by big businesses looking to cash in on the term, and the fear of pesticides is mostly unwarrented. The harshest and most harmful chemicals were banned long ago (think DDT) and today, genetically modifying crops to resist bugs and disease is becoming at least as prominant and useful as chemicals. You're more likely to be exposed to more cancer-causing stuff while talking on your cell phone.
In meat, "organic" and "free range" are also scams; most "free range" chickens live in extremely crowded concrete pens (rather than cages), not in the green pastures of Happy-Rainbow-Farm. For a cow to be "grass fed," the farmer need only feed the cow a certain percentage of low-protein roughage-- it's extremely unlikely that the cow is on actual pasture.

Anyone who actually cares about the source and content of their food buys directly from a local farmer they know; anyone else shouldn't bother with "organic" products.

organic farmers do use pesticides but unlike conventional pesticides they break down in 48 hours or less and are made from natural, not synthetic ingredients. See http://www.omri.org for the list of pesticides that can be used on certified Organic farms. But organic growers look to control pests and not eradicate them (as this is an impossible thing to do) and so they use many more strategies than reaching for a poison and going to town spraying bugs. We also use exclusion like row covers, beneficial insects (and other critters like spiders, snakes, birds, etc.,) to control pest bug populations. we grow soil (literally, it is one of the most important things an organic grower does) and know that healthy soil means far less pest and disease pressure on the crops. we hand pick insects, we use crop rotation, we use trap crops

Are organic crops better than conventional crops/food? I say yes as you don't get GMO's with organics and there is a growing body of peer reviewed evidence that says organically grown crops do indeed have more nutrients than conventionally grown crops. You also don't have the use of synthetic fertilizers and insecticides that too often run off the fields and cause contamination to ground water and the air.

Why does Organic cost more? Several reasons; Supply and demand-there is much more demand than there is supply. Organic agriculture is much more labor intensive than conventional agriculture and human labor costs a lot more than chemicals. The inputs tend to cost 2x or more than conventional inputs

A lot of pesticides you cannot wash off such as the Bt in Bt crops which occur in every cell of the plants and a lot of pesticides are absorbed into the food

These sites have a lot of information about how food is grown organically
http://www.organicconsumers.org
http://www.rodaleinstitute.org

FYI the e-coli going on in Germany/The EU has NOT been linked to organic cucumbers, that was just a rumor. And if it were organic food causing this problem than we would already know exactly where the food came from and how it was contaminated as with organic regulations there must be a paper trail kept for everything sold that tells you what field it was planted in and exactly what inputs (including outside contamination) were used on the area. not to mention raw manure is heavily regulated with organic farms but has no regulation what so ever on conventional farms and yes the conventional farmers use a lot of raw manure on their fields, especially now that the price of synthetic fertilizers has gone up. Currently they have no clue where this e-coli is coming from but you can bet it is NOT coming from any Organic farms.