Does intent matter?
My inclination is to say yes, intent matters a lot. If someone steps on my foot by accident, that's different from doing so maliciously and on purpose. If someone tramples on my emotions by accident, that's different from doing so maliciously and on purpose. In this mode of thinking, I am pretty squarely aligned with Jewish tradition. In Judaism, intentions do matter.
An example: it's a mitzvah (a connective-commandment) to make a blessing over what one eats. If I make the blessing borei pri ha-etz ("blessed are You, Adonai our God, source of all being, creator of the fruit of the tree") over an apple and then eat the apple, then I'm done. If, fifteen minutes later, I decide I'm hungry for a pear too, then I make the blessing again.
However -- if when I made the blessing the first time, I had the intention of eating both fruits, then the blessing "counts" for both and I don't need to repeat it. (My gratitude for this nifty example is due to the author of the post Jewish Treats: Intentions Matter.) When it comes to saying blessings, intent matters.
The same goes for saying prayers. Saying a prayer with whole intention (usually known in Hebrew as kavanah) is a transformative act. Merely reciting words without intention isn't the same at all. The ideal is to carry out a mitzvah -- whether one of prayer, or ritual, or interpersonal interaction -- while holding on to the intent that the mitzvah should take place for the sake of good and for the sake of God. If one walks past a synagogue on the first of Tishri and happens to hear the shofar, but didn't realize it was Rosh Hashanah and doesn't listen to the sound with intention, does it "count" as having fulfilled the mitzvah of hearing shofar? The tradition's dominant answer is: nope, that doesn't count. In order to fulfill a mitzvah, you have to do it with intent. (For more on this: Kavvanah & Intention | My Jewish Learning.)
It's the season of teshuvah, repentance and return. When I think of teshuvah and intention, I think: how do intent and intention impact our need to make teshuvah? And here's where I get back to the idea with which I started this post -- that intentions matter. If I have every intention of lighting Shabbat candles, but I get sick and I can't drag myself out of bed to do the lighting: nu, that's a missing-of-the-mark, but not a big one. If I don't give a damn about lighting Shabbat candles or creating Shabbat consciousness, and that's why I don't bother to light -- that missing-of-the-mark has a different valance, a different feel. It's the difference between failing someone accidentally, and failing them because you can't be bothered to care about the relationship at all.
If I aspire -- if I intend -- to lead a life filled with mitzvot, a life of connection and consciousness, then that intention will shape my days and my choices. I'll still miss the mark, because that's inevitable! But if my intentions are good, then my mis-steps won't be so terrible. This does not mean that one can intentionally sin and then aim to make teshuvah later -- e.g. "I'll ignore this person in need, because I don't feel like being compassionate, but later I'll make up for it." Or "I'm going to say something mean, because I'm feeling spiteful toward this person, but next week I'll make teshuvah and it will be as though it never happened." That's not how it works. We don't get to intentionally sin, promising to get around to teshuvah later. That's a kind of intentional manipulation of the system, and it doesn't actually work most of the time. (That teaching comes from Talmud, Yoma 85b.)
We're called to have the best of intentions, and then to live up to them as best we can... knowing that we'll fall short of our own expectations sometimes, but not letting ourselves off the hook in advance. And -- no matter how good our intentions, we also have to keep the needs of others in mind, and not trample on others in pursuit of our own ends. One could argue that it doesn't matter how good my intentions are; if I stomp on your foot, it hurts you, whether or not I meant to cause pain. Intent matters -- but consequences matter too. The needs of others matter too. For me the first step is always intending not to hurt anyone; intending to do the right thing; intending to be kind and compassionate, to lead a life of mitzvot and connection, always. But I also need to be mindful that I may hurt someone else without intending to do so, and when that's pointed out to me, I need to apologize to the person I have hurt, even if I didn't intend to cause any harm.