I've read a lot about the Symbionese Liberation Army, and the IRA, and the Red Army Faction. I would kind of like to know about other groups that operated in the west during the cold war similar to these, particularly in America and not just one connected to communism. Sorry if this is kind of a broad question.
In the North American case it is worth reading into the Front de Libération du Quebec (FLQ) that operated in Quebec between 1963 and 1970. Furthermore the Oka Crisis of 1990 saw the involvement of militia-like units, again in Canada.
For the European case this is a far easier question to answer on my part. The groups I would recommend you to look into are:
[Anti-Communist]
The West-German Wehrsportgruppen (lit. 'defense sport groups'); neo-Nazi paramilitary associations using sports as cover.
The Lithuanian Rifleman's Union; a currently state-sponsored but privately set up militia association that was involved in the struggle for independence from the USSR both in the early postwar era (1950s), and the post-1989 era.
The Polish Home Army (Armia Krajowa) that resisted both the Nazis in WWII, as well as the Soviets in 1939 and again between 1946 and 1950. Technically set up as a fairly coherent military guerrilla, it does qualify as paramilitary in its later years.
[Left-Wing/Communist]
The Dutch 'Revolutionary Anti Racist Action' (RaRa) that operated in the 1980s and 1990s, and was responsible for a series of bombings of supermarkets, and businesses associated with the South African Apartheid regime. This organisation is interesting for its legacy in politics; controversial politicians like Duyvendak are claimed to have been part of the core of this group.
The Belgian Communist Combatant Cells (CCC). This R.A.F.-like group operated in the 1980s in Belgium and the Southern Netherlands, bombing many Delhaize supermarkets, right-wing party headquarters, as well as planning to bomb NATO military sites.
For reference:
Applebaum, Anne. Iron Curtain: The Crushing of Eastern Europe 1944-56 (London: Penguin Group, 2012)
Carr, Matthew. The Infernal Machine. A History of Terrorism (New York, London 2006)
Crenshaw, Martha. Chapter 13: “The psychology of political terrorism” in M.G. Hermann (ed.) Political Psychology (San Francisco 1986) 379-431
Rapoport, David C‘The Four Waves of Terrorism’, in: Audrey K. Cronin and James M. Ludes (eds.), Attacking Terrorism: Elements of a Grand Strategy (Washington D.C. 2004) pp 46-68
Tony Judt Postwar - A History of Europe Since 1945