Does it matter if I talk or write to Europeans in American English, and vice versa?

No, it doesn't matter. We Europeans can understand what you Americans mean.

There are spelling differences between American and British English. This affected listing of my website on open directory. It was rejected by someone authorized to decide giving reasons of many spelling errors.
I wonder why can't the Americans and Europeans meet to standardize the spellings to be accepted and used by all.
I am an Indian trained with British English, but after participation in Yahoo Answers, I have ended up using both the spellings in the same answer as I get confused which one to use when. If the asker is American, I use "center" and for an Indian, I use "centre", but I often use both in the same answer which looks weird.

Um...can they speak English? If not, you will probably have a problem. If they do speak English, American English and British English are still English, so there should be so problem. Might I advise you to think a little harder before asking qestions like these on yahoo answers.

You'll make more friends trying out a new language.

Europeans are exposed to a lot of American media, so speaking in American English would be fine.

which Europeans had you in mind? People might prefer you to talk to them in their own language, whether French, Polish, Danish, Rumanian, Bulgarian, German.... etc etc. Europe is made up of as number of different countries, one of which is the English-speaking UK.

You;ll find there'll be less confusion if you avoid slang words and terms. But otherwise there shouldn't be too much problem.

nothing wrong in it