It all depends. Mostly on how comfortable I am in a particular environment or with the hosts. Yes, even with family... some family is more comfortable and natural than other family. My mother has never particularly encouraged too much help in the kitchen after, though I'm sure it is appreciated and I always offer. But many times, she declines the assistance.
At my SIL's, I do whatever. At my husband's Aunt's, I do whatever looks like it needs doing, or offer and ask what I can do. Sometimes that's not much, sometimes it's elbows deep in the sink.
At friends, I have always taken my cue from the host. If the host doesn't begin doing any cleaning, and appears to not want to bother with it while guests are still present, then I might offer (and usually they decline) and then let it go.
For myself, when I host family gatherings, with some people I like to sit after and not address the kitchen. With other family groupings (or dependent on the actual meal--some things MUST be put up in the refrigerator for food safety reasons) I want to get right into the major stuff, so there is less to do at midnight (I cannot stand to go to bed with a mess left in the kitchen... nothing shall be left in my sink. Ever. Ugh.).
If I go in and start cleaning up, my mother always asks if she can help, and my MIL often will, too. My SIL's do as well for the most part. I sometimes am grateful for any help I can get, but other times am more protective (?) of my space and would rather work on my own without so many bodies in the kitchen.
But honestly, for the most part, my husband is first up from the table and usually does the major putting away of food and stacking/organizing the dishes/mess before I ever am up from the table. He does most of the "hosting" early, when food prep is being finished up just before serving, and then I take over the "hosting" side once the meal has been served. He chats and socializes while I work, and then we switch.
We didn't *decide* this, but over the years it is what seems to have evolved, and seems to work well for us.
I do have one SIL who always just sits after the meal. But her kids are usually most helpful. :)