Never spinned. And it is spun in the perfect tense. "I have spun" Span in the preterite "I span" seems to be used by UK speakers but not US, but even then only rarely. Span appears increasingly archaic. Spun is the by far the most common usage. "The car span out of control" seems correct to my ears, over the often-preferred "spun". This discussion provides intersting context: http://www.englishforums.com/English/SpanVSpunAsThePastOfSpin/hzxrk/post.htm
i have never come across anyone using 'span' as any sort of past tense for 'spin'... not in the us, nor in the uk, or any other english-speaking country, most of which i have lived in, or traveled in extensively... nor in any contemporary writings by english-speaking natives of same, although dictionaries do note that it is an archaic usage... so, 'spun' is the only past tense you should use imo, if you don't want to be corrected for a typo, or misspelling, or poor grammar...
The link I provided suggests that perhaps "span" is now treated as a variant, rather than used specifically in certain cases. This could be true, I don't have the research to back it up. I can confirm however that here in the North of the UK it is used, for example in "the car span out of control". Though, still agreed that "spun" is by far the most common past tense and ought to be most users default choice.
Better late than never... I'd say 'span' but wouldn't write it. It's often pronounced this way in the UK but like Maia I've never seen it even in a British English dictionary, only spin--spun--spun. A span is a period of time, anyway: He has a short attention span or His acting career spanned forty years.
