Face Death with Dignity: "The Duck Doctor" has it happening to Tom. Having no hope to escape a falling anvil, Tom dug himself a grave, blindfolded himself and had a last smoke. Then the anvil hit him on the head, making him fall inside his grave, which made the dug Earth jump onto him, completing the burial and then the anvil fell in a position to serve as a tombstone.
Friendly Enemy: Tom can be very friendly and laidback towards Jerry when not chasing him.
Friendly Enemies: In some shorts, Tom and Jerry actually coexist peacefully, either being forced into conflict by Toms owner insisting on Tom doing his job as pest control since Jerry is technically a pest, if a mostly unintrusive one, or teaming up so that their live and let live situation can continue.
Jerk with a Heart of Gold: He is often empathetic to other animals, especially those victimized by Tom, and tries to help them out. There are also moments he is repentant after going too far with Tom or even teams up with him.
Nice Mice: Zig-zagged. A lot of his nastiness is in provoked self-defense from Tom, but some of it is just tormenting Tom for the hell of it. When it comes to other animals, though, Jerry is pretty universally nice. See Friend to All Living Things.
Not So Different: Though generally more friendly and altruistic than Tom, Jerry can be every single bite as sadistic as him on numerous shorts.
A Taste Of Defeat: Jerry usually got the last laugh every short. At times however he would lose or come to a bitter stalemate with Tom. These were almost always after he went too far in his retaliation and cost himself his Karmic Protection.
Audience Surrogate: In the sense that she was written to be a bridge between the everyday human world and the insane antics of Tom and Jerry, and is often the only human character present in the shorts she's in.
I Have Many Names: Well, only two, and they haven't been used with much consistency. He was Tuffy in the comics, in the Mouseketeer shorts and some of the later shorts, but in his first animated appearances and in some of his modern ones he goes by Nibbles.
They could also be two different mice, since the short Two Little Indians features two young gray mice drawn with the same exact character model as Nibbles.
Silly Walk: One of his trademarks in his classic appearances is that he doesn't walk so much as he runs, and rather stiffly at that, shuffling his feet at a high speed. This trait is toned down for many later appearances, such as the Mouseketeer cartoons, but he still displays hints of it.
Take a Third Option: One iconic short involves Jerry trying to teach him how to steal food and avoid Tom, while Nibbler simply asks Tom politely for food and befriends him instead.
Androcles Lion: He protects Jerry in a lot of shorts after Jerry does him a favor.
Bad Cop/Incompetent Cop: Some argue that instead of going after Tom, he should be guarding the house which is his job. TV Trash pointed out that at some point where he was beating on Tom, the house could have been robbed. In any case, he usually fails to notice Jerry causing problems, well intentioned or not.
Just Whistle: Makes this arrangement with Jerry on occasion, after Jerry gets him out of some sort of trouble.
Nice Guy: Surprisingly. In episodes that feature all three of them starring together, Spike will usually be played as a lot nicer than either Tom or Jerry but constantly being forced to get angry. When there's an option to put aside their differences he's usually be all for it, if not the one trying to enforce the peace.
Papa Wolf: Spike mellowed somewhat when they added his son, Tyke. But if you mess with him...
Wild Card: Spike is usually a very neutral force - he only wants to be left alone and will only go after anyone (usually Tom, but on the rare occasion this can also include Jerry) if they bother him in some way, which leads to many of his appearances having him be an Unwitting Pawn as Jerry leads Tom do anger him. Likewise, he usually only helps someone (usually Jerry) if they help him in some way first. A few episodes have him being a danger to both Tom and Jerry, with Jerry being crafty enough to avoid pain while Tom is not.
Driven to Suicide: In Downhearted Duckling, where just because he thinks he's ugly, he attempts to cut himself in half with an axe, and later tries to force Tom to eat him (and Tom is more than willing to oblige before Jerry stops him).