mine is only 8 months, but i usually let her play by herself for a chunk of time, and will continue as she gets older. the things i think we'll probably do together? art (but because i'm an artist and will take any opportunity to play with crayons!) and cooking, and maybe some building stuff, cause i find it fun too. i even have a pretty extensive bakground in child development and have played with kids as part of my job, and enjoyed it, but i still don't find it necessary to be my dd's playmate.
my mom never played with us. she was there if we needed ideas or someone to explain our stories too, but she never got involved in our actual play (more than once or twice that i recall). that would have seemed really weird to me! i think the only one of us she ever really actively played with was my youngest sister, but she has developmental delays, so a lot of that was more therapy related. even then, as soon as she could walk and get around by herself, she was out playing with us, and my mom went back to doing whatever it was she did all day!