This year I will not save anything as this was a lost year, but in previous years I saved the next seeds successfully:
rucola, mustard, all cabbages, pumpkins, squash, various tomatoes, chives, various beans, peas, lettuce, leek, melon, peppers, chillis, cress and cape gooseberries.
i actually save the seeds of everything that goes to seed, but some will not germinate for unknown reasons. I was once told that some pumpkin/squash varieties are bred to produce sterile seeds. Don't know if that is true, though.
And as for the hybrids: I like surprises!
I mark the seeds saved from F1s and sow them when there is a leftover space.