All of things being equal, having a degree will improve you job prospects and not having one will significantly limit the jobs that are available to you.
First, there are a number of companies (typically Fortune 1000) that will generally not higher internal software developers unless they have at least a Bachelors degree. You might be able to get in and work there as a contract on the grounds of you skills alone, but the internal policies might prevent you from getting a job if they say you must have a degree.
Second, companies do filter applicants automatically on the basis of what they applicants say on their CV and you may have to do more leg work in order to get your CV in front of a person whom can bring you in for an interview.
Third, it can be used as an excuse to pay you less money once you get a job. This will generally only apply to large companies as smaller companies will understand that some really good developers do not have a degree. However, a number of companies will pay on you the basis of what the "market rates" are and in generally, a person with a degree will make more money than someone without a degree.
Fourth, it helps in regards to office politics. Again, this is likely more of an issue with big companies than with smaller ones, but in fields where a degree is more or less expected, there is an expectation that your supervisor will have at least the same degree as yourself, thus, once you have been in industry for awhile you may encounter office politics if you do not have a degree but are supervising people that have degrees or advanced degrees. Likewise, this is part of the reason why you see people go back for an Masters or an MBA after being in industry for a couple of years - they are trying to move up the career ladder and the extra degrees are unofficially mandatory for the movement.
Now for the disclaimer: there are exceptions to every rule and you will encounter developers that do not have a degree but are doing extremely well, but for every story like this there are developers that go back to school so they can get the "check box item" taken care of and start advancing their careers. Additionally, more often than not, where you go to school does not matter so much as just getting the degree, there are some limited cases where having a degree from a given school might get you head hunted, but once you get that initial job you are going to find that most people don't care.