Gemara

R. Yehudah Nesi'ah collected for needs of a wall. He said that Chachamim must also pay.

(Reish Lakish and R. Yochanan): Chachamim do not need to be guarded (so they need not pay)!

Rav Nachman bar Rav Chisda imposed a tax on Chachamim.

Rav Nachman bar Yitzchak: You transgressed Torah, the Nevi'im and Kesuvim! It says "Af Chovev Amim Kol Kedoshav b'Yadecha", "Gam Ki Yisnu va'Goyim Atah Akabetzem", "Minda Velo va'Halach La Shalit Lemirma Aleihom';

(Rav Yehudah): Mindah is the king's tax. Balu is head-tax. Halach is Arnona.

(Rav Yehudah): All must contribute towards doors for the walls, even orphans, but not Chachamim, for they do not need protection. All must contribute towards digging Pasya, even Chachamim. This is only if they hire others to dig. If they themselves dig, Chachamim are exempt (it is below their dignity).

(Rav Asi): Everyone must contribute for planks (for the wall), even orphans, but not Chachamim, for they do not need protection.

The Kaiser imposed a tax on the city of Tiverya in order to buy a crown. The Amei ha'Aretz asked Rebbi to obligate Chachamim to pay also, and they threatened to leave otherwise. Rebbi refused, and half of them left. The Kaiser pardoned the city from half the original demand. The remaining Amei ha'Aretz demanded that Chachamim also pay, and threatened to leave. Rebbi refused, and they all left, except for one launderer. The officers imposed the entire tax on him. He left, and the Kaiser totally pardoned the city.

Nedarim 62b (Rava): A Chacham may say 'I will not pay the head-tax.' "Mindah, Balu, and Halach will not be placed on them (Kohanim)";

Sanhedrin 27b: Rav Papi brilliantly saved Bar Chama from a dreadful punishment. Bar Chama paid Rav Papi's head-tax for the rest of his life.

Rishonim

Rif: Arnona is conscription (the king takes things for his service), or a meal that people must make for the king when he passes by.

Rashi (8a DH Arnona and DH l'Karya): Arnona is an annual tithe of all animals and produce. Pasya is wells for water.

Rambam (Hilchos Shechenim 6:6): We collect all needs of guarding the city from all residents, even from orphans, but not from Chachamim. They do not need to be guarded. The Torah guards them. Chachamim do pay for fixing roads and streets. If everyone goes out himself to fix it, Chachamim do not go with them. They should not disgrace themselves in front of Amei ha'Aretz.

Rambam (Hilchos Talmud Torah 6:10): Chachamim are exempt from conscription and from any tax, whether it is on the entire city or on each individual.

Rosh (1:26): All must contribute towards digging Pasya, i.e. fixing the city square, even Chachamim. R. Yosef ha'Levi learns from our Gemara that Chachamim are exempt from all taxes and conscription imposed on the Tzibur, whether or not they are fixed. This is only if Torah is his profession. If not, he is liable. It seems that if a Chacham has a small profession or does a little business to support himself, but not to become rich, and whenever he is free he returns to Torah and learns constantly, this is called that Torah is his profession.

Poskim

Shulchan Aruch (CM 163:4): We collect all needs of guarding the city from all residents, even from orphans, but not from Chachamim. The Torah guards them. Chachamim pay for fixing roads, but if everyone goes out himself to fix it, Chachamim do not go, lest they be disgraced in front of Amei ha'Aretz.

Shulchan Aruch (YD 243:1): Chachamim do not go out themselves to build or dig things needed for the city, lest they be disgraced in front of Amei ha'Aretz. Since they are exempt, they need not hire others in their place.

Beis Yosef (CM 163 DH v'Chosav Nimukei): The Nimukei Yosef (Bava Metzia 64a) exempts Chachamim even from hiring others in their place, and says that Tosfos agrees. The Mordechai (Bava Basra 475) says oppositely in the name of Maharam.

Shulchan Aruch (2): This is when everyone goes out himself. If they do not, rather, they hire others in their place, or they collect from residents to do it, if it is needed for living, e.g. wells for water, Chachamim must give their share.

Rema: If at first they went themselves, and afterwards they retracted and hired others, Chachamim must give their shares.

Shulchan Aruch (ibid): Chachamim need not give at all for things needed to guard the city, such as walls, towers, and guards' wages. The Torah guards Chachamim. Therefore, they are exempt from all taxes and conscriptions, whether they are on the entire city or on each individual, whether or not they are fixed. The other residents must pay for them, even what is upon every individual.

Beis Yosef (DH v'Chosav ha'Ran): We exempt Chachamim when the king imposes a sum of money on the Tzibur for the head tax, land tax or Arnona of all the residents together, regardless of the population, and the Tzibur must divide it among them. Then, Chachamim are exempt. If the king fixes a head tax, land tax or Arnona for each resident, then Chachamim must pay. We find in Sanhedrin that Rav Papi used to pay head tax. Also R. Chananel and the Ramban say so.

Beis Yosef (DH Aval and CM 163 DH DH veha'Ramban): The Rosh says that R. Yosef ha'Levi totally exempts Chachamim. In a Teshuvah (15:8) he says so in the name of the Ramah. The Tzibur pays even for rich Chachamim. They are exempt due to Torah, not due to poverty. Also the Rambam says so. I say that there is no proof from Rav Papi. Perhaps the Tzibur used to pay for him, and Bar Chama accepted to pay for him, so he would not have a debt of gratitude to the Tzibur. Or, Rav Papi used to do business to get wealthy, and Torah was not his profession, therefore he was not exempt from head tax! Or, Rav Papi was very wealthy, and voluntarily paid head tax, and Bar Chama accepted to do so for him!

Beis Yosef (ibid., DH v'Lich'orah): The Tur says that R. Yosef ha'Levi and the Rambam hold like the Rosh, who always exempt Chachamim in every case. Perhaps this is not so. They exempt when the tax is fixed, i.e. on the Tzibur, but not when a sum is fixed for every individual! However, R. Yosef and the Rambam did not distinguish. It seems that they always exempt.

Beis Yosef (DH Kosav ha'Rashbatz, citing the Rashbatz): If a city hired a Chacham and many need him and he ignores all his affairs to do their needs, even R. Chananel and the Ramban exempt him from head tax.

Shach (3): The Nimukei Yosef and Ramban say that Rebbi did not have power to force the Amei ha'Aretz to pay. If not, he would not have allowed them to leave.

Gra (3): The episode with the crown proves that Chachamim are exempt even from a tax that is not fixed.

Gra (4): There is no proof from Rav Papi. The Tzibur used to make him pay improperly, just like the Amei ha'Aretz fled to avoid paying the Chachamim's share of the crown. This is why Rav Papi was not concerned for bribery, like the Rosh (Sanhedrin 3:17) says.

Rema: Even if the king said that Chachamim themselves must give, the Tzibur must pay for them. If the Tzibur made a Cherem obligating Chachamim to pay, the Cherem is Batel. A Chacham may make a Cherem and excommunicate to force the Tzibur to pay for him, whether he is rich or poor.

Shulchan Aruch (ibid): This refers only to a Chacham whose Torah is his profession. If not, he is obligated. However, if he has a small profession or does a little business to support himself, but not to become rich, and whenever he is free he returns to Torah and learns constantly, Torah is his profession.

Shach (7): This is not only if he finances himself minimally, rather, just to support himself, but not to become rich. R. Tam is lenient about taking Ribis from Nochrim, for nowadays 'everything is needed to survive', for the king taxes us. This does not apply to a Chacham who does not pay taxes!

Beis Yosef (DH v'Chasuv): The exemption is only for "Kedoshav", but if he disgraces Mitzvos and lacks Yir'as Shamayim.

Rema: He need not head a Yeshiva; he must be established to be a Chacham in his generation who knows how to debate in Torah, and understands by himself most places in Talmud, its Perushim and rulings of the Ge'onim, and Torah is his profession. Even though nowadays there is no Chacham to receive a litra of gold (if one embarrasses him), we are not so particular about exempting from taxes. In any case, the custom in some places is to exempt Chachamim from taxes, and in other places the custom is not to exempt them.

Shach (8): This is as long as he is a Chacham in his city. He need not be important among Chachamim elsewhere (Binyamin Ze'ev 252).