I need help compiling a list of fig tree varieties that do not require the fig wasp to produce quality crops. I believe this would be a helpful resource for those new to figs who want to get into the hobby. 

I will start with these:

Brown Turkey
Texas Everbearing
Celeste


Thank you all

In this forum unless it says "Smyrna" type fig, then it's a common fig and it does not need the wasp. The ones you mentioned above are common figs.
Unless you are in CA where the fig wasp is present, stay away from names such as Bursa, Goklop, Calimyrna(Sari Lop),Marrabout,Snowden or anything coming from a questionable source. A questionable source to me, means a non grower transferring what possibly could be a mislabeled or an untested variety.

Thank you Sas...I live in San Antonio TX and was trying to make sure these figs I am purchasing will grow. Most websites do not say if the figs are "common." Are the figs on the "treesofjoy" website common. I believe those are the ones sold by BASS.

So are the following common figs?

VIOLETTE DU BORDEAUX
DESERT KING FIG
SMITH FIG
BROWN TURKEY FIGS
ALMA FIG
CELESTE FIG
NEGRA D'AGDE
BLACK BETHELEHAM
COL DE DAME NOIRE
TIGER PANACHE
BLACK MISSION
KADOTA FIG
Sumacki FIG
PONTE TRESA

Welcome to the forum. Yes those are all common. You have quite a mix there from the cheapest to the most expensive. From the most readily available to the most highly sought after. There are many many posts in this forum about new people. "Newbies". You will find lots of advice using the search feature. Bass is unquestionably a great source for figs as are many people who post on this forum. You can search that info too. My advice would be to start slow with a couple cheap varieties until you get your technique down. There is a learning curve. Have Fun. Happy Figging!

Welcome Ozarka31. There are hundreds of named varieties and there are many books and articles about them.

For example a Hungarian site has one here. If you scroll down the page you will find the list.

Additionally, Ira Condit's Fig Varieties: A monograph shows an extensive list of varieties sorted and grouped by various criteria.

The 'mother website' of this very forum has a database of varieties here.

You can also find a bunch of information here ;)

Thank you all for taking the time to provide me with this valuable information. It was much needed. 

There are too many to list!

ozarka31
your post no. 3 says desert king is a common fig,
in fact it is a san pedro which needs the wasp for the second crop
having said that it is well worth while having for its large
and excellent first crop.  

Thank you aaa. I had no idea.

Pretty much any variety. If you are not in California, just assume that any variety is a common fig unless otherwise noted