Don't have a budget? Then write a good story.
In the words of director Samuel Fuller:
"What makes a good movie? A story! What makes a good story? A story!"
I've seen movies with little to no budget that have pulled off good stories.
Recent examples would be M. Night Shamylan's movies The Sixth Sense and The Village. Both these films sport no big action scenes or special fx and yet tell very memorable human tales.
Most of Clint Eastwood directed movies would be considered low budjet. High Plains Drifter was filmed in 4 weeks.
A lesser known example would be the low budget movie TimeQuest. A film about a time traveler who creates an alternate timeline by stopping the JFK assasination.
Most Famously would be Star Wars, a low budget movie filmed with models and blue screen. Made with 10 million dollars. The first and greatest blockbuster ever?
What are your thoughts?