This is a topic that is subject to intense and oftentimes personal debate. Because I've been exposed to the hellfire of such debates, my personal policy is to credit the artist if I can (for example, in my signature I credit Starscout for my avatar) if it is a piece of fanart. For a mass-produced piece of art - say for example you took a screenshot of the original cartoon of a character and cropped it to show her - I wouldn't credit as it's mass produced.
As for 'permission', I sought permission on my tumblr for the buttons I made, because I was taking artwork and adding something to it (in this case, text). I gained permission for some whilst others never got back to me, and I highly doubt some corporate places will ever respond but I've placed the credit there in my Credits section anyway.
It never hurts to ask! It never hurts to credit! Some artists will say explicitly no reposting without permission, often with commissions, so you can always double-check of not sure but most are okay with it as long as you a) do not claim the work as your own, b) do not alter it significantly like recolouring or editing and c) do not sell the image for profit.