Can you get a blurry background without expensive lenses?

When I was taking my first photos on a regular smartphone, I was convinced that a blurred background was the exclusive domain of expensive DSLRs with thick lenses. Then I realized that was a myth. It's not about the optics themselves, but how you use them and what you've got in your hands.

The previous answer was right about distance and sensor size, but I'd clarify: it all comes down to focal length and how close you get to your subject. You can shoot a portrait with decent background blur even on a phone if you use portrait mode (if you have it) and get close to the face. On a budget DSLR with a kit lens, you'll get similar results if you set the aperture and distance correctly. But if you're shooting a person from far away in full frame - no amount of optics will save you there, the background will still be sharp no matter what.

In practice, it's pretty straightforward: choose the longest focal length you have, shoot with the aperture wide open (portrait mode on your phone already has this dialed in), and get closer to your subject. If you really want to blur the background for effect - look for lenses with high light transmission, but that's not really in the "without expensive optics" category anymore. For regular shots, what you've got is genuinely enough.