DS is 16 months spends most of his time just playing with his toys, toddling around the house, tormenting the cat, etc but some things he likes to do together are:
Playing with a small football I got from JJB Sports. He throws it and even dribbles it! Before he could walk he used to half-crawl-half-bumshuffle up to it and kick it with an outstretched toe. Very funny.
He likes scribbling with crayons or biros - I tape a bit of paper to the dining table (our dining table is old and knackered so marks don't matter though) and try and get him to stay on the paper.
Having a bath in the middle of the day.
I put reins on him and just let him walk outside, wherever he wants to go, using the reins to avoid falls/roads/dog poo etc.
Those wooden jigsaws with the little plastic knobs on.
Singing songs (even just from the radio/kids programmes) and playing with instruments (bells, maracas etc).
I pull all the sofa cushions off onto the floor and let him crawl around on them. Also let him crawl on me lying in bed, and tickle him lots.
Playing "knock knock" - He stands in a room and closes the door, I knock then open the door carefully and he thinks it's great. (You have to teach them to be careful of fingers first)
TBH as PP said everything is learning at this stage - most of it physical, ie what does this feel like, what happens if I poke this, can I lean on this without it falling over, etc.
"Helping" with the housework is a great one though! DS knows how to feed the cat (though wants to do it 20 times a day), he can put clothes in the washing machine and take them out, and put them into drawers if I tell him which drawer. He can wipe things with a cloth and tidy up his toys. He doesn't always do it, but he can