Most of my humor is deadpan, like Kullervo's. Sarcasm is my friend. And when people don't get it, it's easy to just carry on like normal. If they think it's offensive or something though, then I am obligated to inform them that I, in fact, was joking. "Well it wasn't funny." "Maybe not to you."
On occasion I make more crude/off-color or sexual jokes. I don't talk like that often so it's good when I want to shock people. Things about black heels and black flats, and I suddenly say, "Well I'm white and I'm pretty flat." (Referring to my chest.) The look on the other person's face was priceless.
There was also the time that one of our drum majors was leading a sectional and we were talking about hearing loss in one ear and playing piccolo (both the drum major and I played piccolo at the time). So she asked me about hearing loss and I went, "Huh?" And she repeated her question. It took two or three iterations before she got it. And then I answered her seriously.
Telling actual jokes with set-up and punchline and stuff, I tend to either miss important details or start laughing way too hard in anticipation of the punchline. Back in freshman year, I had a bad habit of finishing the joke and immediately launching into explaining it. I've since remedied that but I sometimes go too far in the other direction where people either don't realize that the punchline is the punchline or they don't get it at all and I have to drop hints until they finally go "oh" or I've fully explained it. That might be the nature of the joke or it might be my delivery.