Depending on the state you live in, you can probably recover damages from the other driver even if your negligent conduct contributed to the accident. Most states use a “comparative negligence” system. In some states the jury simply assigns a percentage of negligence to each driver and this governs the amount of recovery. For example, the other driver ran a red light but you were speeding and this preventing you from stopping in time to avoid the other car. The jury might find that the other driver was 75% responsible for the accident and you were 25%. The result would be that you would be entitled to recover 75% of your damages from the other driver. This is called “pure comparative negligence.”
As of 2012, most other states still prohibit any recovery if you are 51% or more at fault. In the red light example, you would still be able to recover 75% of your damages. But if the percentages were reversed (the jury found you 75% at fault) you would recover nothing. Contrast this with a “pure comparative negligence” state where you would be able to recover 25% of your damages.