As there hasn't been a lot of answers for Sephardi Nusach, i will post all the resources i have found for Sephardi sources:
Egyptian Nusach: Ahaba, Shaarei Shalom, Orah Saddiqim, Karaites.org
The Ahaba website is from an Egyptian synagogue in New York. There are many recordings and videos here. Many. There are several years' worth of Seder Tawhid, an Egyptian Jewish celebration on Rosh Chodesh Nisan (said to have been instituted by Avraham Ben haRambam). Three years of Slichot plus selections from a fourth. Several High Holiday tunes. Several kinot. Havdalah in a whole bunch of different maqamat. Torah and haftarah trope according to the Egyptian minhag (under the Hazzzanout section). All of Esther. Under R' Yosef Hamaoui Media there are even more recordings, including all of Psalms and a wedding service. The Shaare website also seems to have an Egyptian Hazzan, with much simpler melodies. The Orah website is from an Egyptian Karaite synagogue with Egyptian Karaite melodies. The melodies are related to the general Egyptian melodies shared by all Egyptian Jewry. The Karaites.org website has the entire Torah and Haftarah chanted by a new (and very good) Hazzan with very high quality recordings. Many of the melodies are the same as normal Egyptian Jewry, though the Revi'a is quite different.
Syrian/General Sephardic: Sephardic Hazzanut Project, Bar Mitzvah.com, Pizmonim.org, Shituf Piyut
The Sephardic Hazzanut Project contains Syrian and Sephardic recordings. The website went online in 2009 and has regular visitors from more than fifteen hundred cities around the world. It is exciting to see such interest in Sephardic hazzanut and we are very interested to hear about you and your community. As of September 2015, additional recordings and updates will be on the Sephardic Hazzanut YouTube Channel. The Bar Mitzvah website has te'amim lessons according to the Sephardi Yerushalmi tradition, as well as Morrocan and Ashkenazi. The pizmonim website has Torah readings for various traditions, usually giving you the names of the Hazzans. There's lots of material, so it's a lot to sift through. The Shituf Piyut is designed for people to submit their own recordings, so if you search through it you can find lots of interesting recordings, including te'amim.
Italian Nusach: Torah.it
Website is in Italian. Huge archive of Italian recordings, including Italian Torah Reading, Italian prayer nusach, and classes. There's a lot more there than I've been able to properly categorize, wade through if you're interested.
Moroccan Nusach: http://www.tht.co.il/, http://www.orshalommontreal.com/hazanout.html, Te'amim according to Itamar Malka, Te'amim according to the Darke Aboteinu Community
There are actually waaaay too many sources to just provide one link. So i will post various links to websites, as well as various youtube recordings. The Moroccans have done a great job of making an online presence. The Or Shalom synagogue website has two streaming players on the page with Moroccan nusach and music, one of which has a CD that can be downloaded. The one that can't be downloaded has several recordings of each part of the Friday night service, several parts of the Saturday morning service. However, you have to scroll through them to see them. The second player has music from a concert (the CDs can be downloaded, but there's no track information on them), which mostly includes piyutim (a couple from Havdalah) and features instrumental music as well.
Tunisian Nusach: http://www.rebbihaitaieblomet.org/, http://www.chivteisrael.com/piyoutim-hazanout/
The Rabbi Haitai website is for Tunisian synagogue in Paris, with quite a few recordings! I'm not sure why, but under Hazanoute, there are several recordings of the Kaddish and even more of the Kedushah, and they include Shabbat evening and morning. There are also a number of miscellaneous recordings, including piyutim, Sheva Brachot, havdalah, Shabbat morning, Brit Milah tunes, etc. Under Haguimes (Fêtes), aside from Torah and haftarah readings, there's Esther, the Haggadah in several recordings (including in Judeo-Arabic), Ruth, Eichah, and Slichot. Under Autres passages, there's Shir Hashirim, more Haggadah recordings, and a few other things like haftarah blessings and the Shema. The Chivtei Israel website has lots of recordings in the Tunisian, Moroccan, and Yerushalmi rites. There's also a few Egyptian songs there.
Iraqi Nusach: http://www.hibba.org/en/allmusics,
The first website hibba has lots of musical recordings. The spice readers website has the te'amim according to Saeed Jalali, cantor at a an Iraqi synagogue in Los Angeles called Kahal Joseph. The last youtube video is a zarqa table according to the Iraqi tradition and Sephardi Yerushalmi tradition according to Moshe Chabusha, a world renowned Iraqi Chazzan. After the Zarqa table he does a proper reading of the Shema.
Yemenite / Temani Nusach: http://www.temoni.org/?cat=4, http://www.moryapp.co.il/
The Temoni.org website has lots of avrious recordings, but the entire website is in Hebrew. The Moryapp website has the weekly Torah and Haftarah reading in high quality with a scrolling Hebrew text that makes it easy to follow.
Libyan Nushach: Sfatai R'nanot
The website is Hebrew. This is an institute for the preservation of the traditions of Libyan Jews, and there are lots of recordings often with texts. There are Torah readings, but i've been unable to find a Zarqa table thus far. But they are organized on the side menu, and there is a search feature as well.
London and Amsterdam Sephardic Nusach: S&P Central
A big hub for various websites of the London and Amsterdamn Sephardic tradition. Follow the links to their various websites to get to the recordings.