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On Earth, the planet itself is negatively charged and the clouds are positively charged, causing lightning to travel from the clouds to the surface. While there are significantly smaller wisps of lightning that reach from the Earth to the clouds and the bolt that is travelling down, would it be possible to have a planet in which the charges are reversed, causing lightning that arcs from the planet to the clouds?
If possible, how would this different charge affect an Earth like planet?
TL;DR: Lightning in our world can possibly do both, so there probably wouldn't be much of a change.
Lightning is a form of static discharge caused when an excess of electrons exist in one location (e.g. the ground) and a lack of them (e.g. in the clouds). This would result in, if enough potential energy (voltage) existed in the electrons, a discharge in the form of lightning from the negative to the positive.
In the scenario you give, what we actually would have is lightning going from the negatively charged planet to the positively charged clouds! As far as I understand it, lightning going from ground-to-cloud or cloud-to-ground are both entirely possible on Earth, it just depends on how the charges are split. It's also why clouds often have lightning strikes between them (distances are shorter, potential energy required for an ark is less, hence ZAP). HOWEVER, the typical strike is in fact due to "feelers" of negative charges extending downward from the clouds. The bottom of a storm cloud is typically negatively charged, and the ground is typically positively charged below it.
To answer your question, both would be possible, thus I do not see why you couldn't have the convention between them change. If you're building a world, a little hand-waving can get around most physics things (ooo, magic), especially when science itself doesn't understand the phenomenon 100%.
Some additional reading:
http://en.wikipedia.org/wiki/Lightning
https://www.ec.gc.ca/foudre-lightning/default.asp?lang=En&n=9353715C-1
https://earthscience.stackexchange.com/questions/580/why-does-lightning-strike-from-the-ground-up
Lightening is a discharge to balance the electrical charge that has built up between objects, (the earth and clouds, or between clouds etc.) Lightening can travel in either direction already here on Earth. The ground is not 'positive' and the sky is not 'negative'. Regions get an imbalance and the ground could have the negative charge or to put it more correctly the sky could have a more positive charge and thus attract a lightening strike from below.
