I know the extreme animal rights activists could be considered “left wing”, but there doesn’t seem to be many other liberal terrorists about. Are us Liberals in general letting our side down with our wimpish nature, or merely showing our overwhelming common sense and decency?
Google, and ye shall find.
Various Communist outfits around the world are usually considered “left wing”, and some of them have engaged in terrorism. Here’s a famous example.
They seemed to have reached a heyday in the 70’s, but there are a few still around. For example
The Provisional IRA’s stated goal was to establish a socialist state in Ireland.
All the Irish Republican terrorists, as far as I know, had a socialist agenda behind their murder campaigns.
In the US or anywhere in the world? The recently publicized FARC should qualify. Both our Republican and Democratic presidential nominees have called them terrorists.
I seem to recall a rather absurd thread here, wherein it was argued that Al Qaeda was left wing. I forget who held that point of view.
The following groups designated as terrorist by the US State Department list of Foreign Terrorist Organizations are generally considered “left wing”
The Abu Nidal Organization
Basque Fatherland and Liberty (ETA)
Communist Party of the Phillippines/New People’s Army
Continuity Irish Republican Army
The Kurdistan Workers Party
The People’s Mujahedin of Iran
The National Liberation Army of Colombia
Palestine Liberation Front
Popular Front for the Liberation of Palestine
PFLP-General Command
The Real IRA
Revolutionary Armed Forces of Colombia
ELA of Greece
Revolutionary Organization 17 November of Greece
Revolutionary People’s Liberation Party-Front of Turkey
Shining Path
You mentioned the animal rights people in the OP, but it should be noted that they are the most active group of terrorists in England–above Muslim extremists. So I don’t see that there’s much cause to worry that your side isn’t doing its part.
I was going to ask, “Why are there no Liberal suicide-bombers”, but looking at the list Captain Amazing has provided, I think I’d have been way off-beam! 
p.s. I meant “left-wing”, not “Liberal”… I know they are not exactly inter-changeable!!!
Not on Captain Amazing’s list are some well known historical terrorist groups that made quite an impression, such as the Rote Armee Fraktion in West-Germany and the Brigate Rosso in Italy.
The Irish National Liberation Army too.
There’s the “ERF” (Earth Liberation Front). I think they’ve burned down a few Humvee dealerships and McMansions in California.
There’s no such thing as a Humvee dealership, the Humvee is a nickname for the HMMWV, which the “H1” or “Civilian Hummer” is based on. “Hummer” dealerships sell H2s and H3s which are not connected to the military vehicle at all, and only bear a superficial aesthetic resemblance to them.
And then, of course, Nepal has just recently just taken over by the Communist Party of Nepal who used a combination of terrorism and armed force against the government to achieve that goal.
Was it because they hate Republicans? 
uh, umm “E-L-F”
::Backs away::
Don’t eat my world…
Greenpeace.
Unless Paul Chadwick lied to me in Concrete: Think Like a Mountain, I think that was a group called “Earth First!”
(Double-checking, I may be getting that mixed up with an article I read about the ELF)
In any case, Earth First! may or may not make your list, depending on who you ask.