The Red Army Faction (Baader Meinhoff gang)
The Red Brigade
The Angry Brigade
The IRA
The Mau Mau
The ANC
I wasn't entirely sure what was meant by 'non religious inspired terrorism'. Of course, there has been a lot of terror attacks that had nothing to do with religion (or atheism, for that matter).
Ultimately, terror attacks I'm aware of have been inspired by some sort of positive belief...something that atheists can/do of course have and can be motivated by.
The RAF for example, were largely motivated by anti-fascism, with their own flavour of left wing political views heavily influenced by the particulars of German post-war politics.
The Mau Mau is a strange group to include as an example of 'non religious' terror, though. The nature of the oath was pretty deliberately structured in a ritualistic and religious way. Still, they had clear motivations that had little to do with religion, so perhaps that's what you meant?
The ANC...well, much like the Mau Mau, there were legitimate grievances against pretty gross colonial oppression. That doesn't justify all actions taken (particulary in the case of Kenya) but nationalism is a powerful force when combined with a minority government.
The Angry Brigade reference confused me a little. Sure, they're terrorists, but from memory they killed no-one, and in fact deliberately tried to limit damage. Anyways...no dramas, just not used to seeing them in a list with groups like the IRA, or the Mau Mau.
So...I guess you're just saying not all terror is religiously motivated? I'd go further and say the majority is politically motivated.