I finally went through and compiled information from my own experience and from labdoor.com to come up with a top-brands list mostly for my own reference. A lot of brands have similar names and logos so with my memory there is no chance I would remember.
Note: the supplements most likely to be ineffective across the board are multivitamins and green tea supplements. Most likely to have an inaccurate label are non-vegetarian omega-3s. Most likely to be contaminated (usually with arsenic) is magnesium. Dr's Best and Pure Encapsulations have a safe magnesium: I would not recommend buying from anyone else without research! This includes all my favorite brands.
Brands I will try from without necessarily checking amazon reviews:
Jarrow Formulas (tested by independent third party lab),
Nature's Bounty (tested 3rd party, in-house & by labdoor),
Pure Encapsulations (tested by labdoor and independent 3rd party)
Solaray (tested in-house & by labdoor),
Solgar (tested in-house & by labdoor),
Source Naturals (tested in-house & by labdoor),
Swanson (tested by independent third party lab & by labdoor).
Brands I will look for, but will check reviews before buying:
Bulk Supplements (tested by labdoor),
Dr's Best (tested by labdoor),
Garden of Life (tested by labdoor),
NatureMade (tested by labdoor),
Nature's Way (tru-ID tested & by labdoor),
NatureWise (tested by independent third party lab & by labdoor),
Now Foods (tested by labdoor).
I've contacted all the above brands about their 3rd-party testing and will update if they say yes they do.
One exception is KRK Supplements, who is the only brand I trust for choline, because I can feel when it works or not.
* vouched for by me and labdoor and/or 3rd party labs, tested in my body multiple times (NONE of these make a good magnesium-only product):
(I vouch for their evening primrose oil, borage oil, vitamin D3, and phosphatidyl-serine)
"We use several outside labs that at intervals conduct testing on our products. They are Convance, Silliker, and Eurosins." (I vouch for their biotin, cranberry, b-12, b-6, evening primrose oil, odorless garlic. I use but don't necessarily vouch for their calcium-magnesium-zinc.)
(I vouch for their magnesium and amino acids)
(I vouch for their zinc, iron asporotate, copper, astragalus, pau d'arco, echinacea. I sometimes use but don't necessarily vouch for their calcium-magnesium asporotate.)
(I vouch for their biotin, glucosamine, b-6, glutamine, and vitamin e)
(I vouch for their b-12, b-6, beta carotene, evening primrose oil, vitamin e, and zinc)
(I vouch for their vinpocetine, oregano oil, and l-serine 500) Honestly I'd buy much more from them if they weren't so expensive.
~ vouched for by labdoor and/or third party labs and okay by me:
3rd party lab tested (I vouch for their garlic and cranberry)
(good source for magnesium!) (I vouch for their vitamin D3)
(I vouch for their glutamine, odorless garlic, pau d'arco, glucosamine)
(labdoor gives them almost all A's) (I vouch for their glutamine)
(great EXCEPT calcium-magnesium) (I vouch for their evening primrose oil, borage oil)
(I vouch for their chewable probiotics)
(good EXCEPT magnesium) (I vouch for their echinacea)
Garden of Life
(I vouch for their meal replacement protein powder)
^ not tested by labdoor but okay by me:
AbsorbHealth ^ (I vouch for their vinpocetine)
Raw Barrels ^ (I vouch for their glutamine)
` tested well by labdoor but I have not tried it:
Country Life `
Life Extension `
Nutridian ` (only biotin has been tested)
Nutrigold ` (good EXCEPT bacopa)
Nootropics Depot `
Pure Science `