I've been having an issue with my phone, when I'm trying to charge. My cellphone doesn't start charging, when the charger plug is on wrong position inside the socket. I have to move my plug degree by degree to get battery charging. Is it a sign of broken socket? I have tried also different chargers.
Assuming you have a phone with micro USB connector. You could try this http://forum.xda-developers.com/showthread.php?t=1856180
Micro USB ports tend to loosen over time because of their crap design (Which won't be a problem with USB type-C which will hopefully become the new standard for phones).