Antonym of "apathy"
I'm looking for a word that describes a general feeling of concern for things. Preferably not with a negative connotation (ie. neurotic), but for use as a description of someone who expresses interest in and wants to change things around them.
Dictionary.com gives: interest, care, concern, feeling, passion, sensitivity, sympathy, and warmth. These all feel specific though. You can say someone is generally apathetic, but if you say that a person is generally interested, caring, etc., those have very specific implied meanings (interested ~ interested in something specific, caring ~ cares for others).
For starters, the way the word apathy is formed according to etymonline gives a hint at what the antonym should be:
apathy (n.) Look up apathy at Dictionary.com c.1600, "freedom from suffering," from French apathie (16c.), from Latin apathia, from Greek apatheia "freedom from suffering, impassability, want of sensation," from apathes "without feeling, without suffering or having suffered," from a- "without" (see a- (3)) + pathos "emotion, feeling, suffering" (see pathos). Originally a positive quality; sense of "indolence of mind, indifference to what should excite" is from c.1733.
So if apathy describes the absence of pathos, then pathos is the opposite...
Alas, pathos, and certainly the adjective pathetic, have acquired quite a negative connotation, and it will not be generally understood any more as feeling, passionate.
So for words that do somehow, in a general way, describe that somebody is actively feeling about things around them, I would suggest passionate as an option:
having, showing, or expressing strong emotions or beliefs.
It seems interesting, when we look at the origin of passion, again on etymonline), that pathos has moved from general (if sometimes suffering) emotional engagement towards a negative, mainly suffering meaning in English, whereas passion, originally mainly meaning suffering, has moved towards a more general, and certainly nowadays positive meaning: I don;t think that most speakers of English will associate someone's passion for human rights with the passion in the passion of Christ.
My best guess to what you might be looking for:
Empathy:
the action of understanding, being aware of, being sensitive to, and vicariously experiencing the feelings, thoughts, and experience of another of either the past or present without having the feelings, thoughts, and experience fully communicated in an objectively explicit manner; also : the capacity for this
In this way you could say one is generally empathetic.
You might consider engaged:
From Dictionary.com:
1. busy or occupied; involved: deeply engaged in conversation.
I focus on the involved aspect here to meet your need for showing interest and wanting to change things around them.
For example: While Amy used to be quite apathetic, after taking the course she has become deeply engaged in teaching and in fact has become a role model to several new students.
Also consider joie de vivre, which means “Enjoyment of living; happiness, ebullience, zest for life.” [wiktionary]
It's rather more elegant than life curious (which was mentioned in a previous answer).