No need to think about the rules of grammar, the easiest way is to just delete "and my friends", and see if the resulting sentence is correct: - Last weekend me __ organized some outdoor activities (no, that's not right) - Last weekend __ I organized some outdoor activities (that works, so just put "and my friends" back in)

The second sentence is the more correct one. The grammatically correct pronoun is 'I', because this is part of the subject of the sentence (nominative case). However, I'd be reluctant to say that the first sentence is actually 'wrong'. Why? Because hundreds of millions of native speakers use 'me and ..' in this way. I use it myself in informal conversational contexts. Strictly speaking, it doesn't follow the rules of formal grammar, because 'me' is an object pronoun. It's OK to say this informally, but not when you're taking a grammar test or writing a formal text.

Hello Attila. I´d say: Last weekend some friends and I organized some outdoor activities. Because 'me" cannot conjugate a verb. "ME" is a reflexive pronoun and it´s used as the direct and indirect object of a verb or of a preposition. I hope it helps.

The second one would be correct.

I is correct whenever you are talking about both yourself and others.