Not without an education, no. But without a formal education, yes.
There is programming knowledge that is categorized horizontally (problem-solving, logic, software architecture, OOP, security, etc.) and vertically (iPhone, *NIX, CICS, bash, PERL, XML, etc).
There's also industry-specific knowledge you need to familiarize yourself with. Health care. Automotive. Systems Programming. Scientific computing. ERP. Manufacturing. etc.
But the key here is to realize your primary education is to acquire the skill to sell yourself.
One of the first facts a salesman learns is you don't win over the person with the checkbook, you win over the person who controls the person with the checkbook. HR manages the legal and administrative details of its relationship with employees. You don't want to go through HR unless you want to write programs for HR.
You've got to hit the department with the need for the type of programs you want to write. Instill in them the emotional bond that their future success requires them to get you on-board (which, once you've taken the time to learn what they do, how they do it, and their culture, won't be hard).
Take the time to develop a lot of practical software that applies to the department and industry you want the job in, for the programming environment typical in that industry. Plus a few more in related departments/industries/environments. And one or two in unrelated ones.
Odds are managers already know what graduates are like. You've got to be the iPhone of programmer candidates. The new, shiny that already fits into their culture and industry.
For end-user application development, become acquainted with their products and learn their features and their bugs. Learn it better than their salesmen. (It's a big bonus if you're familiar with their competitor's products too.) Hang out with their customers, and see what their needs are and how they use the software. Then go to conferences, user groups, networking events where salespeople interact with potential customers.
Salespeople have been known to varnish the truth. Don't call them out on it (publicly) and don't torpedo the sale. Listen to what objections prospects have about the product and how sales handles them. If you make a suggestion for a feature that the customer really wants you can ingratiate yourself to the sales department, and they can exercise their pull to get you hired. Because $$$ (or your local currency) makes the decisions. So don't torpedo the sale.
Maybe you find a hole in their product that you can fill by writing and selling your own product. Then they buy your company. That's another way to end up hired by a company without having a formal education.