I think the Carter administration's incident in the late 1970's is more accurately characterized as an "oil crisis" because there were real shortages, serious enough to alter trends in car purchasing habits, warranting economy automobile redesigns (smaller, lighter, more efficient, no more muscle cars). Gas stations actually ran out of gas, resulting in hours long waits on miles long lines, and theft by siphoning forcing the introduction of keyed locks on gas tanks.
These were real problems people faced, although it wasn't exactly a full panic.
Oil "scares" on the other hand were threats that raised eyebrows, and caused dramatic price fluctuations in anticipation potential problems. Each "scare" really only hit the wallet and bank account, without altering real behavior.
In that sense, yes, there were a few other "scares" between Jimmy Carter and present day. Each grouping came periodically, maybe every ten years. Almost all of them were tied to Iraq.
The first was the invasion of Kuwait in 1991. I think gas prices blew past $2/gallon for the first time.
The second was 9/11, and $4/gallon gas starting late 2001. This one was rough. Pretty much everyone I knew was groaning about gas prices, and with Iraq invasion rumors people started thinking $5 would break them.
The 2003 Iraq invasion actually resulted in a downward trend (due to international theft or spoils), but it's ever been below $2 again, and it's been back up to $4 at the pump, here and there, depending on geographic region and state taxes, here and there.
With the 2008 meltdown, oil prices weren't displaying any gouging, and there wasn't much of a scare at the 2001 decade mark, because as others have mentioned, fracking has buoyed domestic production.