I read somewhere recently that moms unknowingly reinforce clingy babies (not that this is you, but just an idea).  We have a tendancy to secretly love that our kids want us over everyone else and this causes us to react in ways that causes our baby to continue to be clingy.  Anyway...start with distracting your baby when he wants you to pick him up.  Tell him no, you are busy with dinner (or whatever) right now so he needs to play with his toys.  Explain that you still love him and you aren't going anywhere but he needs to let you do some things.  And then stick to it - if you walk off and he cries...let him.  You know he's not in any danger because you're not far away and crying is ok (it's terribly heartbraking, but just tell yourself that he's doing it because he's trying to get you to do something different than what you say you're going to do).  Then, you can also try leaving him with dad while you clean up the house...and that means leave him with dad even if crying starts.  Leave the house if you have to, but dad has to fend for himself...he'll figure it out.  

I had this problem early one with my child and then I realized I was doing everyone an injustice because I was using my kid to make me feel good!  Now daddy does things the way he wants and I leave them alone.  My child happily plays by herself.  Just like eating healthy, sleeping well, manners and everything...you have to teach your child not to be clingy.  Children have to be taught EVERYTHING.  He may always be a momma's little boy, but teaching him to be more independent will be invaluable when it's time for him to leave the house!

Good luck!  I hope you find the "problem" and have the patience to fix it.