The 1980s were a really popular time for government shutdowns:
This chart comes from Tammy Frisby of the Hoover Institution. (Click to enlarge.)
Note that in the 1970s, gaps in funding didn't mean that the federal government had to physically shut down. That practice only started in the 1980s, after then-Attorney General Benjamin Civiletti argued that the Anti-Deficiency Act required government agencies to close up if their funding expired. Since then, a lapse in funding has meant an actual, tangible shutdown.
Previously, Dylan Matthews went through all previous government shutdowns, why they happened, and how they got resolved.
Update: On the other hand, if you want to see how rare government shutdowns actually are in the broader scheme of things, check out this chart from Seth Kadish:
(Via Walter Hickey.)