I know that I may not eat general wine from the store (as opposed to wine that's certified kosher). Can I also not derive other benefit from it? Specifically: Can I give it as a gift to a non-Jewish neighbour?
I once asked at an ask-the-rabbi site, though I don't remember which one, whether I could "re-gift" a bottle of non-kosher wine I'd been given. I was told that it was ok to pass the bottle along so long as I made it clear that I was passing along something I'd received but could not use. (In other words, don't pretend I was being especially generous by buying the recipient something.)
In searching for support for that suggestion I found: the Institute of Dayanim says you may pass it along, and they give the following citations:
See Tur, Shulchan Aruch, and Rema, Yoreh De’ah 123:1, where two opinions are cited concerning today’s idolaters.
The Shulchan Aruch 124:6 permits deriving benefit from wine made by a non-Jew who we know does not worship idolatry; the Taz 123:2 is lenient where a loss is involved. See also Shoel Venishal 6:142; Ben Ish Chai Balak 4; Yashiv Moshe 1:203.
The CRC says it is controversial but there is room for leniency. They do note a stringency, though they seem to be talking about purchasing such wine as a gift and disposing of an unwanted gift might be different:
Wine (or grape juice) which was poured in an idolatrous service is known as yayin nesesch and is assur b’hana’ah. In addition, there is a Rabbinic prohibition against drinking any wine which a non-Jew touched; this wine is known as stam yayin and there is a difference of opinion as to whether it is or isn’t assur b’hana’ah. Rema (YD 123:1) rules that l’chatchilah one should adopt the stricter opinion but in a case of great loss one may be lenient.
Accordingly, not only may one not drink non-kosher wine, brandy, cognac, or a beverage sweetened with non-kosher white grape juice concentrate, but one may not purchase a bottle to give to a non-Jewish business associate as a present. The reason is that when one gives a present it generates good will, and in that context the giver of the present is (also) considered to be benefiting from the gift. Therefore one may not give issurei hana’ah as a gift to someone else.
Since the matter is controversial, I don't think it would be wise to actually buy such wine (with the intent of giving it as a gift). But if you happen to have some already, it looks like there are alternatives to pouring it down the sink.