The Ben Ish Hai (Rabbi Yosef Haim of Baghdad, 1833-1909), in Parashat Tazria (16), codifies the obligation to wash one's hands without reciting a Beracha before eating a food that has been dipped in one of the seven liquids. These liquids are: wine, blood, olive oil, milk, dew, honey and water. The Ben Ish Hai mentions that a helpful way to remember these seven liquids is through the acrostic "Yad Shahat Dam," the letters of which are the first letters of the seven liquids ("Yayin," "Dam," "Shemen Zayit," "Halav," "Tal," "Devash" and "Mayim"). This Halacha is most familiar to us from the Seder on Pesah, when after Kiddush we wash our hands without a Beracha in preparation for eating the celery dipped in salt water. As water is one of the aforementioned seven liquids, before eating celery with water one must wash his hands without a Beracha. Similarly, if a person washes a fruit and eats it without drying it, he must first wash his hands just as he does before eating bread three times on each hand but without a Beracha.
There are, however, a number of conditions that apply to this obligation:
1) Although the Ben Ish Hai held that this obligation applies to even small quantities of food, Hacham Ovadia Yosef, in his work Halichot Olam, Helek 1, Parashat Tazria, writes that one may be lenient when eating less than a Ke'zayit of food dipped in liquid. Though it is certainly commendable to be stringent in this regard, according to the strict Halacha one who eats less than a Ke'zayit of food with liquid is not required to first wash his hands.
2) Some authorities maintain that this obligation does not apply to food eaten with liquid that had been cooked, while others extend the requirement even to such cases. Furthermore, some authorities contend that washing is required only if one eats the food with his hands, whereas others claim that the obligation applies even when one uses a utensil. As for the final Halacha, the Ben Ish Hai and Hacham Ovadia Yosef rule that one may be lenient in situations where both of these factors apply, meaning, when one eats food with a cooked liquid, with a utensil. Thus, for example, if a person lifts a piece of cake with a fork and dips it in coffee (which consists mainly of water), he is not required to wash his hands, since the coffee has been cooked and one eats the food with a utensil.
3) There is some controversy concerning a case of one who eats with his hand but his hand does not come in contact at all with the liquid. The Hid"a (Rav Haim Yosef David Azulai, 1724-1807), in his commentary to the Haggadah entitled Simhat Ha'regel, disapproves of the practice of many to dip cake into their coffee and eat it without washing their hands. According to the Ben Ish Hai, the Hid"a refers only to those who submerge the cake entirely in the coffee, such that their hand inevitably touches the coffee. If, however, one's hand does not come in contact with the liquid, he need not wash his hands. Rabbi Moshe Halevi (Israel, 1961-2001), by contrast, held that the Hid"a's ruling applies even if one's hand does not come in contact with the liquid. As for the final Halacha, Hacham Ovadia Yosef concurs with the position of the Ben Ish Hai, and thus one is not required to wash his hands if his hand does not touch the liquid.
4) The Ben Ish Hai further writes that one is not required to wash his hands if the food he eats is customarily eaten with a utensil. Thus, for example, one need not wash his hands before eating cereal with milk, even if the milk has not been cooked. Since nobody eats cereal and milk without a utensil, the obligation of hand-washing does not apply. Similarly, if one eats a salad that people normally eat with a utensil, he is not required to wash his hands even if olive oil is mixed into the salad. However, if one eats large pieces of vegetables with olive oil, he must wash his hands even if he uses a utensil, since some people would eat large pieces of vegetable with their hands. Similarly, if one eats a wet pickle he would have to wash.
5) It should be noted that this obligation does not apply to foods eaten with oils other than olive oil. Therefore, one generally does not have to wash his hands before eating "Sufganiyot" (jelly donuts), since they are usually not made with olive oil.
6) One who drinks one of the seven liquids with his hands or finger is not required to first wash his hands. Although the Ben Ish Hai rules that one should preferably wash his hands in such a case, Hacham Yishak Yosef, in his work Yalkut Yosef, Helek 3, notes that the prevalent custom does not follow the Ben Ish Hai's ruling. Thus, one who drinks water from a faucet with his hands is not required to first wash his hands. Likewise, many Rabbis have the practice after reciting the Berachot under the Hupa (canopy) at a wedding to spill some drops of wine onto their finger and then sip the wine off their finger. In such a case, one would not be required to first wash his hands.