Unfortunately you will need to be a ittle more specific -- you can collect "regular social security" based upon the simple fact that you have reached a certain age. It becomes a little more murky when you wish to collect disability because you cannot work, but unemployment laws require you to be actively seeking employment. Some Administrative Law Judges have really picked up on that difference and will not allow someone who is applying for social security disability collect unemployment benefits while they are claiming they cant work to one government agency and having to actively seek employment for another government agency.
If you are talking about Supplemental Security income -- then unemployment would put you over the income threshold to collect SSi while collecting unemployment.
A pension is pretty much the same way -- it is most fo the time derived by an age criteria so it should not effect social security. It may effect SSI in that the income/assets would not allow someone to have a pension and SSI at the same time.