When the fast of the 17th of Tammuz ends, in Kew Gardens Hills, New York, 2011

If you live elsewhere, you cannot simply rely on these times. You should go to the linked websites and check out the time for your particular zip code. Also note that this is for this particular year. It is not the same time, precisely, each year.

The Etz Chaim Bulletin has:
Fast of 17 Tammuz    begins 4:28 AM; ends 9:05 PM




















According to Chabad.org, it is the middle number here:

Shkiah (sunset)	8:23 pm
Fast Ends	8:55 pm
Tzeit Hakochovim (nightfall)	9:02 pm

And according to MyZmanim:

Fast Begins at 3:57 AM Dawn - Degrees or at 4:27 AM Dawn - Fixed Minutes Eating of a settled character - אכילת קבע - may not be started during the half hour immediately preceding dawn. Please consult your Rabbi for details.  Fast Ends R' Tukaccinsky The fast ends no later than the emergence of ג' כוכבים בינונים at - 8:58 PM R' Moshe Feinstein One who finds fasting difficult may eat at - 9:02 PM One who does not find fasting difficult should wait until the time for מוצאי שבת at - 9:11 PM ?מהיכא תיתי

(The time given for Rabbi Tukaccinsky is typically 3 minutes more than the Chabad time, for the following reason they give:

* 3 minutes have been added to compensate for the fact that the שקיעה times (for ירושלים) printed in ר' טוקצינסקי-'s luach, are 2 to 3 minutes later than the times for "sea level שקיעה". Definitions provided by other Poskim may also be subject to a similar translating.
)

I wonder whether the 9:05 given by the Etz Chaim bulletin is similarly a 3 minute shift to R' Moshe Feinstein's zman.

Now, I have given three times. Which one do we hold like? More importantly, which one do you hold like? Ask your parents, or your local Orthodox rabbi, to see how you hold in general.

What can I add? Oh, yes. Here is what gives me mild discomfort about the fast of the 17th of Tammuz, in particular. To cite Wikipedia regarding the Sumerian deity Tammuz -- the name of the month, Chazal tell us, was adopted by the Jews on their return from Bavel:

In Babylonia, the month Tammuz was established in honor of the eponymous god Tammuz, who originated as a Sumerian shepherd-god, Dumuzid or Dumuzi, the consort of Inanna and, in his Akkadian form, the parallel consort of Ishtar. The Levantine Adonis ("lord"), who was drawn into the Greek pantheon, was considered by Joseph Campbell among others to be another counterpart of Tammuz,^[1] son and consort. The Aramaic name "Tammuz" seems to have been derived from the Akkadian form Tammuzi, based on early Sumerian Damu-zid.^{[citation needed]}The later standard Sumerian form, Dumu-zid, in turn became Dumuzi in Akkadian.

Beginning with the summer solstice came a time of mourning in the Ancient Near East, as in the Aegean: the Babylonians marked the decline in daylight hours and the onset of killing summer heat and drought with a six-day "funeral" for the god. Recent discoveries reconfirm him as an annual life-death-rebirth deity: tablets discovered in 1963 show that Dumuzi was in fact consigned to the Underworld himself, in order to secure Inanna's release,^[2] though the recovered final line reveals that he is to revive for six months of each year (see below).

In cult practice, the dead Tammuz was widely mourned in the Ancient Near East. Locations associated in antiquity with the site of his death include both Harran and Byblos, among others. A Sumerian tablet from Nippur (Ni 4486) reads:

She can make the lament for you, my Dumuzid, the lament for you, the lament, the lamentation, reach the desert — she can make it reach the house Arali; she can make it reach Bad-tibira; she can make it reach Dul-šuba; she can make it reach the shepherding country, the sheepfold of Dumuzid

"O Dumuzid of the fair-spoken mouth, of the ever kind eyes," she sobs tearfully, "O you of the fair-spoken mouth, of the ever kind eyes," she sobs tearfully. "Lad, husband, lord, sweet as the date, [...] O Dumuzid!" she sobs, she sobs tearfully.^[3]

These mourning ceremonies were observed even at the very door of the Temple in Jerusalem to the horror of the Israelite prophet Ezekiel, whose Biblical prophecy expresses Yahweh's anger at His people's apostate worship of idols:

"Then he brought me to the door of the gate of the Lord's house which was toward the north; and, behold, there sat women weeping for Tammuz. Then said he unto to me, 'Hast thou seen this, O son of man? turn thee yet again, and thou shalt see greater abominations than these." —Ezekiel 8:14-15

Ezekiel's testimony is the only direct mention of Tammuz in the Hebrew Bible.

Mourning for Tammuz is a cult practice, and one that even extended to the Jews, until the time of Churban Bayis Rishon. Yes, we have our own reason for fasting, but no explicit mention of a reason is given in Tanach. Rather, in Zecharia 8:19, it is referred to as 'the fast of the fourth month', and the gemara fills in the rest of the details.

Update: I'll add to this post some halachos of the fast, from the 5th Avenue Synagogue:

I. Nature of the Fast

The first questioner asked a series of questions: What is the nature of the obligation to fast on the Tenth of Tevet? Under what circumstances may one be lenient? For example, if a soldier is on standby or positioned on the border, though there is no danger right now, may he omit fasting because he could be called into action? Is there a difference between eating and drinking? May one shower?

A. Bathing

The answer said that Asara B’Tevet and the other minor fasts (Shiva Asar B’Tammuz and Tzom Gedaliah, with Ta’anit Esther in another category because it is not a mournful occasion) are not treated as strictly as Tisha B’Av, in that the only prohibition is eating and drinking, and the other afflictions (refraining from washing, anointing, leather shoes, and marital intimacy) are not observed. Some say that people of high religious spirit should be strict even on the minor fast days, citing the Bach, who said we do not see people bathe on the three minor fasts. R. Rabinovich concludes that this is not a proof, because the Bach lived in an era when it was uncommon for people to bathe other than on Erev Shabbat. Even according to the Bach, in years when Asara B’Tevet falls on Friday, one should bathe. In our era, when people are accustomed to a daily hot shower, we do not see people impose a stringency against bathing on the Tenth of Tevet. R. Rabinovich added that, especially for soldiers, whose exertions cause perspiration, to be stringent would be acting strangely. Finally, he cited the Aruch Hashulchan, who said that even according to the Bach one may wash in cold water or take a sauna.