Badass: Has played quite a few of them, most notably Qui Gon Jinn in The Phantom Menace and Bryan Mills in Taken. Henri Ducard /Ra's Al Ghul from Batman Begins counts as well.
Badass Baritone: Has a distinct deep, somewhat gruff voice. Though hilariously inverted in The LEGO Movie, where Bad Cop is how he usually sounds and Good Cop is a silly high-pitched voice.
Badass Grandpa: After a career of mostly heavy dramatic roles, Taken abruptly transformed him into a regular action hero at age 56.
The Big Guy: He's 6'4", and often towers over most of his castmates. Appropriately, he was cast as Michael Collins in the film of the same name-Collins was called "the Big Fellow" for his height. In fact, he's so tall that Qui-Gon Jinn action figures almost throw the other figures out of scale. As Qui-Gon, he's also the only Jedi whose robe has a seam down the back. Because of his height, they couldn't make the robe out of one piece of fabric because bolts of cloth don't come that wide.
They also had to spend thousands of dollars making the walls of the sets taller before they could start filming, because apparently the set designers didn't realize just how tall he was.
Ooh, Me Accent's Slipping: While a wonderful actor, he might be the poster boy for this trope when attempting anything other than his native Irish. Both he and Harrison Ford have an especially egregious case of this in K19: The Widowmaker, which explains that cutaway joke on Family Guy about kids not knowing about sex ed being as lost and confused as Liam Neeson trying to do an American accent.
That said, he does normally tone his accent way down in most of his films. In real life his accent is much, much stronger and a touch harder.
Papa Wolf: His role in Taken was a quite brutal version of the trope, in which an ex CIA agent goes to huge extremes to save his kidnapped daughter from being sold into prostitution.
Ain't the only time, either. He's played Jean Valjean of Les MisÚrables (1998), a role in which being Papa Wolf is a requirement.
Playing Against Type: A mild version — in the fact-based drama Five Minutes of Heaven, the Roman Catholic Neeson played a Protestant killer (and the Protestant James Nesbitt played the Catholic brother of his victim). Both actors are actually from Northern Ireland.
Also, any time he plays the villain. It's not very common. This is specifically why he was chosen to be Ra's al Ghul in Batman Begins, because they thought it would shock fans that Liam was the true villain.
In The LEGO Movie, he plays Bad Cop/Good Cop. He usually isn't as mean as the former, and not as nice and wimpy as the latter. He still pulls it off, though.
The Troubles: Has done roles encompassing both the all-Ireland Troubles of 1919-1923 and the Northern Ireland Troubles of 1969-1998.
In Ireland, Neeson is primarily known not for Schindler's List, or even Star Wars, but for Michael Collins, which was not widely seen abroad but was a huge, huge hit with Irish viewers, since Collins is often considered a national hero there.