How many slices are required to make you responsible to wash on Pizza?
The opinion of Harav Moshe Feinstein zt”l holds two slices makes you responsible to wash.(I believe this would be the Main Psak (Halachic Ruling) for American's)
Harav Shlomo Zalman Aurbach zt”l, and Harav Elyashiv say any Pizza would require one to wash and bentch (V'zos Habrocha page 230).
Rav Belsky Shlita Rosh Yeshiva of Torah Voddas and Posek for the Orthodox Union says
two slices would only be a meal if they are eaten with something else, such as a knish. While I personally ascribe to 3 each person should seek Rabbinical counsel for this and all other question.
Square otherwise known as Sicilian pizza which is made by first baking the dough and then adding the cheese is always Hamotzei the same applies to Pita-Pizza made by taking a Pita and putting cheese and Ketchup on it the Bracha also maintains it's Hamotzie status.
The above is a summary of a recent Halachicly Speaking article available here: http://www.ladaat.net/siteimages/fl_4c1258431c6eb.pdf
Please refer to the final halacha in b'tzias hapas. The Shulchan Aruch rules that pashtida (dough filled with various fillings including meat, fish or cheese) is hamotzi even as a snack. The Mishna Berurah distinguishes this from pas haba'a b'kisnin in that the latter is mainly baked as a treat whereas pashtida is eaten for satiation. He says it's no different than a meat sandwich You just put the meat on before baking, but the intent is the same. I will let the reader opine for himself where pizza falls in.
According to those who hold that pizza is Pat Habaah BeKisnin, Rabbi Jachter suggests, based on a Biur Halacha, that the amount required for washing should vary based on gender and age. The money quote:
"It should be noted that the Biur Halacha (168b s.v. Af Al Pi) asserts that the “objective standard” varies from group to group. He specifically mentions a distinction between young and old people. Thus, if an older individual plans to eat an amount of Pat Habaah BeKisnin that most older people consider to constitute a meal, he must recite Hamotzi even though a younger person would view that amount of food as merely a snack. Rav Daniel Wolf of Yeshivat Har Etzion (Yeshivat Har Etzion’s Daf Kesher volume 6) suggests that a distinction can be made between men and women regarding this matter, as men generally eat more than women. I have often wondered whether adolescent boys should be considered as a distinct group regarding this matter as well, since they tend to eat more than most other people. Personally speaking, I considered three slices of pizza to constitute a meal when I was a teenager, and as an adult I consider two slices of pizza to constitute a meal."
However, he notes that most disagree with this view entirely, including Rabbis Mordechai Willig, Ovadia Yosef, Yisroel Belsky, Zalman Nechemiah Goldberg, and Hershel Schachter, requiring a Hamozti even on one slice of pizza.
The full article can be found here: The Bracha on One Slice of Pizza
I thought that commonly pizza dough in the US was made mezzonot(so that one would need to eat the necessary shiur to pass into it being considered a meal).
Whereas pizza dough in E"Y is typically made as lehem and thus one slice needs washing.
Some kashrus orgnazations require apple juice in dough not all
Maran writes (Hazon Obadia Tu Bishvat, Berachot) that if the dough is made with butter or oil (as opposed to water) you should make Mezonot as long as you're not eating a Shiur of Keviat Seuda. However, if you can't taste the sweetness than you make Hamosi.
Or Lesion writes (vol. 2 pg. 97) that no matter what the dough is made of if the sauce is melted into the dough after the baking the Beracha becomes Mezonot.
I asked a few Talmide Hachamim if Hacham Ovadia would agree to that Or Lesion and they said he wouldn't.