My most frequently used (both La. and general) Internet resources:

Ancestry - Aside from the usefulness of census searching in my pajamas at midnight, I've found several cousins through Ancestry and shared info and photos.  If your budget is tight, use it at a local library or LDS (Mormon) family history center.

FamilySearch - Use the search boxes or click on the map to see a list of collections by country.  Check out the Louisiana records, especially the Louisiana Deaths Index, with some extracted info (not complete) to 1956. For index info from 1956-1963, or to order copies of death certificates, see the state link below.  Use your imagination and wild cards and search on various spellings, especially for French names.

La. Secretary of State - La. Death Records (index and ordering) - Order death certificates from 1963 and earlier for $5 each.  (La. death certificates are available only to next of kin for records less than 50 years old).  Though there is less info available online in these indexes than with the extracted info at the FamilySearch site above, the info can still be helpful even if you don't order a certificate. Comparing the info at both sites can help you find possibly mistranscribed, misspelled or misrecorded names. (Add Ancestry's La. Death Index for 1900-1949 for a third option.)

Find A Grave, occasionally - cemetery transcriptions, and also photos at the first site. (Or try LA GenWeb parish pages, Louisiana Cemeteries or Cemeteries of LA, among others. More of my relatives just tend to be at Find a Grave.)

Google searches - Use full names in quotes, try "last name, first name" also, try using initials, add a place name &/or the word "genealogy" if the name is common. Try spouses' names together with "and" in between. You'll find a surprising number of message board posts and family trees. Don't forget to search Google Books as well.

WorldConnect family trees at RootsWeb - many family trees, but use info as a guide, not a substitute, for your own research.  This goes double for trees without sources (or if the only sources are other trees or GEDCOM files) -- same goes for Ancestry and FamilySearch trees.

Louisiana GenWeb - lots of free info contributed by fellow La. researchers. If you have North La. roots, check out the cemetery transcriptions.

U.S. GenWeb - the national page, where I go when faced with a new-to-me location

WorldCat - library searches for many libraries at once. Not all libraries belong, but you can see what books might be in a nearby library or available for possible interlibrary loan.

Cyndi's List - categorized, annotated links to almost anything genealogical online

Linkpendium -  great genealogy links from the folks who started RootsWeb.

More Internet goodness: 

52 Weeks of Online American Digital Archives and Databases: Louisiana  -  from Miriam Robbins, who writes the AnceStories blog.  See her "52 Weeks" series for resources in other states, as well.

Louisiana Online Historical Directories (by parish) - also from Miriam.

Louisiana Online Historical Newspapers (by parish) - ditto.

Los Angeles Public Library - my local "big library" catalog, which has access to newspaper databases and HeritageQuest online for library cardholders. It also has a lot of La. genealogy books and books on Southern U.S. genealogy, which was a pleasant surprise.  Many big-city libraries often have great resources you can access from home if you have a library card.  Check your local public, college or university libraries for their offerings.

Southern California Genealogical Society - my local genealogy society & library. Despite its SoCal location, it has an impressive French-Canadian collection and very good Acadian and Louisiana sections. Check with your local society to see if they have a library or a collection at a local library.

Louisiana Genealogy Blogs - La. genealogy events & news, bloggers, cemeteries, surname contacts, MANY La. genealogy links at the bottom of the home page.

Genealogy Guys and Genealogy Gems - excellent general genealogy news & tips podcasts. Learn about genealogy while listening to the online broadcasts via your computer, iPod or other MP3 player.  Podcasts are available through links at the sites above or via iTunes.

Cajun/Acadian Internet resources:

Acadian-Cajun Genealogy & History - The late, great Tim Hebert's exhaustive how-to site.

The Cajuns - Stanley LeBlanc's site, which I wrote about here.

Acadian and French-Canadian Ancestral Home - extensively researched site by Lucie LeBlanc Consentino, which I wrote about here.

CanadaGenWeb - including Acadian, New Brunswick, Nova Scotia and PEI GenWeb sites.

Acadian , Acadian-Cajun, and Acadian/French-Canadian mailing lists on RootsWeb - Search the list archives for your names; odds are your ancestors have already been discussed. Join a list and make some new genealogy friends. (Parish (county) lists and surname lists can also be helpful.)

New Orleans Internet & offline resources:

New Orleans Public Library - New Orleans genealogy links (There is also a good general genealogy links list following the NOLA links.)

Greater New Orleans Archives Directory - from, appropriately enough, Greater New Orleans Archivists

Colonial Louisiana Research (at LA GenWeb)

Guide to African-American Research in New Orleans - from the African American Resource Center of the New Orleans Public Library

African-American Internet resources:

Afrigeneas - Big repository of links, message boards, news, records, how-tos for African-American research.

Afro-Louisiana History and Genealogy, 1719-1820 - free online database of records compiled by Dr. Gwendolyn Midlo Hall

Louisiana GenWeb Archives, African-American records - area of the LA GenWeb site devoted to African-American records from Louisiana in particular, though records are also available on parish pages

Manuscript Resources on African-American History in LSU Hill Library's Special Collections - various records, papers, collections of family papers, historical memorabilia, etc.  Try searching by family name, slave owner name, place, or plantation name -- you never know what you might find. 

Great secondary sources (mostly books) I've used for researching Cajun, Acadian, and French-Canadian ancestors:

For my families in Acadia:
Stephen A. White, Dictionnaire généalogique des familles acadiennes: Premiere partie, 1636 à 1714, 2 vols. + English supplement, Moncton, BC, CANADA: Centre d’Études Acadiennes, Université de Moncton, 1999. (currently out of print but in many libraries)

That's Genealogical Dictionary of Acadian Families, Part 1, 1636-1714, by the way, often referred to by its French acronym, "DGFA." It's THE authoritative source for Acadian genealogy, and yes, it's written in French, but an English supplement translates the notes, and the genealogical info isn't hard to understand. Keys to the sources are a bit more difficult to understand, but worth it to figure out. The volumes contain meticulously researched genealogies, census info & historical notes about each family.

White also updates and corrects the dictionary in a free, almost-200-page PDF available here and is working on Part 2, the Acadian families after 1714. He'll be working on it quite a while, as it's projected to be a 10-volume series, according to the Center for Acadian Studies site.

Also provided at the Center's site are links to PDF genealogies for the first generations of prominent Acadian families.  Mr. White published this research (via the Acadian Historical Society's journal) for the 37 families who hosted reunions at the World Acadian Congress in 1994.  For this reason, you may sometimes hear the work referred to as "37 families."

For my Quebec families:

René Jetté, Dictionnaire généalogique des familles du Québec des origines à 1730, Montréal: Les Presses de l’Université de Montréal, 1983. (Genealogical Dictionary of Families of Quebec from its Origins to 1730, available in some libraries.  Also known by its French acronym, "DGFQ."  See Beauregard’s corrections, as well, below)

For some Quebec & France info:

The free website Genealogy of the French in North America by Denis Beauregard. He also sells CDs containing all the website material and then some, with complete source info.

For my La. Cajun families (especially, but not exclusively, Catholics):

Rev. Donald J. Hébert, Southwest Louisiana Records, 47 volumes, Baton Rouge, LA: Claitor's Publishing, 1974- (Church & civil records to 1915)
(Claitor's Publishing now publishes or distributes most titles formerly produced by Hebert Publications)

(For SE parishes, try Hébert's South Louisiana Records volumes.  The late Rev. Hébert also published many other books having to do with Cajun and Acadian research.)

For my earliest South La. families (Once you've worked backwards in time through the Hebert volumes--or if your ancestors lived in the regions around New Orleans or Baton Rouge--try these compilations):

Rev. Msgr. Earl C. Woods et. al., Sacramental Records of the Roman Catholic Church of the Archdiocese of New Orleans, 19 vols., New Orleans: Archdiocese of New Orleans, 1987-2003. Records covered run from 1718 through 1831.  Vol. 2 (1751-1771) is currently (Aug. 2014) out of print.

Renée Richard, Emilie G. Leumas et. al., eds., Diocese of Baton Rouge Catholic Church Records, 22 vols., Baton Rouge, LA: Diocese of Baton Rouge, 1978- . (Order forms at the link, or check Records span 1707 to 1905 and include records from Grand Pré in Acadia before the Acadian expulsion, and early Pointe Coupée in colonial Louisiana.

In the past few years, two volumes were added to this series for individuals without surnames (mostly those who were slaves): Pointe Coupée Records, 1770-1900: Individuals without Surnames, and East and West Baton Rouge and the Felicianas Records, 1800-1880: Individuals without Surnames. 

The most recent DOBR publication, Baptisms, 1901-1905, (vol. 23?) is available on Amazon, as are other selected volumes, some in e-book format.  Some paper volumes formerly available from the diocese are currently out of print; check the websites for current availability as the diocese may be going to a more print-on-demand way of doing things.

For only a few of my families, but these filled in some vital info:

Albert J. Robichaux, Jr., German Coast Families: European Origins and Settlement in Colonial Louisiana, Rayne, LA: Hebert Publications, 1997. (Most Hebert Publications items are now available through Claitor's Publishing.)

Albert J. Robichaux, Jr., The Acadian Exiles in Nantes, 1775-1785, Rayne, LA: Hebert Publications, 1994.

Albert J. Robichaux, Jr., The Acadian Exiles in Saint-Malo, 1758-1785, 3 vols., Eunice, LA: Hebert Publications, 1981.

Albert J. Robichaux, Jr., The Acadian Exiles in Chatellerault, 1773-1785, Eunice, LA: Hebert Publications, 1983.