My non-spoilery thoughts on the last Harry Potter: I think Rowling was going for 'senseless and horrible' in her almost random knocking-off of characters, but it just came across as gratuitous.
A fictional death that I think achieved 'senseless' very well (and I'll talk about it here because I think the whole show has aired pretty much everywhere) was Tara's in Buffy the Vampire Slayer. She started out very shy and stifled, and her personality bloomed when she fell in love with Willow. Then she had a falling-out with Willow and they ended up as not-a-couple for most of a season. Finally the thing that had separated them was resolved and they got back together, and it looked like happily-ever-after for them -- and Joss Whedon was so good at making people really, really want these characters to be happy -- and then Tara was killed, in a way that nobody expected or could have prevented.
Of course, from a plot perspective her death was not 'meaningless', as it set off a whole chain of events that lasted for the rest of the show, due to Willow's anger and grief. But in context, it was the worst way to go -- she didn't die saving someone's life or doing anything else important, and she was killed by a guy with a gun, of all things (instead of something supernatural, which our heroes understand and know how to fight).
It seems to be hard to express 'senseless' death in fiction. In real life there's a certain feeling of meaninglessness when someone dies in a way that was preventable, or if someone dies while doing something that they never would have thought of as dangerous. But in fiction you have to set it up more, and I think it's okay to use some poetic license to create a situation where, for example, you think this character is going to have a happy ending -- and then you kill them.
Also: keep in mind that you don't want to draw too much attention to the character by setting them up to die, because readers will predict what's coming. Just do your best to make the readers feel for all of the characters what you want them to feel. If you do a particularly good job of making people love the character who is going to die, it won't stick out like a big neon arrow, and the audience will feel it more when it happens.