Let's say you have a $50\%$ chance of going to the club on Friday and $30\%$ chance of going on Saturday, then (assuming the events are independent), the probability of going at least once on the weekend, which I'll call $P$, is $P=1-0.5\times0.7=0.65$.
Now let's say the events are dependent; if you go on Friday, you're $10\%$ less likely to go on Saturday. Does $P$ increase, decrease, remain unchanged, or is there not enough information?
Let $E_1$ be the event that you go on Friday and let $E_2$ be the event that you go on Saturday. We then have $$P = \mathbb{P}(E_1) + \mathbb{P}(E_2) - \mathbb{P}(E_1\cap E_1).$$ Like you said, if $E_1$ and $E_2$ are independent, then $\mathbb{P}(E_1\cap E_2) = \mathbb{P}(E_1)\cdot \mathbb{P}(E_2)$, giving $P = 0.5 + 0.3 -0.15 = 0.65$. But $\mathbb{P}(E_1\cap E_2)$ can be any number less than $0.3$ since $E_1\cap E_2 \subseteq E_2$. Say you pledge to never go to the club on both days (that is, $E_1$ and $E_2$ are mutually exclusive -- very not independent). Then $\mathbb{P}(E_1\cap E_2) = 0$ and $P = 0.8$. On the other hand, say you pledge to only go on Saturday if you went on Friday as well. Then $E_2 = E_1\cap E_2$ and $P = 0.5$.
The short of it is that it depends on how your events depend on each other.