David Wain, the director of sleeper comedies Wet Hot American Summer, Role Models, and Wanderlust thrives on a low budget. "The lower the budget, the more fun it is to do... Sometimes those obstacles spark creative solutions." There's plenty of evidence supporting Wain's theory to be found not only in his own films, but in some of the most iconic movies of the last 50 years.
When you have a huge budget to rely on, it can induce laziness in the filmmakers, because every expensive shortcut is made available to you. You typically can't just throw money at a project and expect innovative results - just ask George Lucas - especially in today's age of overinflated budgets. One superhero movie now costs more than all of the Best Picture nominees from the 1980 Academy Awards combined, it's easy to forget that movies can still be made on the cheap.
In fact, some of the most memorable elements of incredibly iconic films were only made possible because there wasn't enough money in the budget to do things the way they were supposed to be done.