How does signup/registration form length impact conversion?

Form length is definitely important (as is the *perception* of form length), and you should make your forms as short as possible, but there are three big variables that are more important than length.

The most important variable is motivation. People who are motivated are extremely likely to fill out a form...that's the first and best place to start when designing forms. (it's likely that motivation happens before the form is even seen...so creating a motivating onramp to the form becomes critical)

The second one is reducing friction in ways other than length. This is where copywriting is so crucial. I'm a huge proponent of microcopy, or small bits of copy that get people over hurdles to sign-up and other processes. For example, telling people who are about to buy that they don't have to create an account when using Paypal is a huge one...for many years you did in fact need to create an account. I've written more about that here: http://bokardo.com/archives/writ...

Third, the information you ask for is crucial. The fields on your form have to make sense to a user who is filling it out. For example, most forms fail because the people who made it require inappropriate information, such as your telephone number when all you want to do is purchase, or your credit card information when all you want is to make a free download. In other words, not all form fields are created equal. They have to seem appropriate for the task.

Finally, it should be noted how important brand is to filling out forms. People are wary of filling out a form for a brand/company/product they aren't familiar with, but every day Google/Amazon/Apple/eBay get millions of people to fill out forms that are much longer and more involved than necessary. These companies have built up trust over time and so have a much easier time getting people to fill them out.