polysyndeton - n. the rhetorical use of several conjunctions in close succession, especially where some might be replaced with commas. The adverbial form of the word is "polysyndetic."
While the device is often used by children - "And then Billy ran outside and he threw my doll on the roof and he laughed at me and he's a brat" - it occasionally makes its way into prose. Here is an example cited by Wikipedia from Ernest Hemmingway in After the Storm :
"I said, 'Who killed him?' and he said 'I don't know who killed him, but he's dead all right,' and it was dark and there was water standing in the street and no lights or windows broke and boats all up in the town and trees blown down and everything all blown and I got a skiff and went out and found my boat where I had her inside Mango Key and she was right only she was full of water."