Which credit bureau predominantly do car dealers check when buying a new car?

My score differs from each credit bureau. Can I request that they check a specific one?

Both of those answers are wrong. there are three credit bureaus yes. equifax, transunion and experian. there is no set answer as to which bureau do dealers use. i generally pull equifax and transunion, mainly because those are the two bureaus that my banks use most. i deal with about 13 different banks and they vary on which bureau they like. some lenders will use multiple bureaus most of the time the one w/ the highest score to get it to score the best in their system and get the best rates/terms. chrysler defaults to transunion, toyota defaults to equifax. wells fargo defaults to transunion but all three will use the other two bureaus. in louisiana experian is the default bureau for most lenders. amsouth, trustmark, national, capital one all prefer and usually only pull equifax, citifinance pulls either transunion or equifax , but their system defaults to whichever bureau has the most trade lines.. chase, americredit, drive all use transunion.
as far as the bureaus go themselves. there are different versions of each bureau. car lenders specifically pull an auto based bureau. housing pulls a housing based bureau. when you pull your own credit it is a general bureau, not focused towards any specific lending institution. we pull equifax 5.0 auto, and transunion auto 04 which is what most of my lenders use. but you wont be able to pull those w/out dealers licenses.
last but not least. credit scores themselves dont always make the final decision for the banks when it comes to financing or rates. most have internal scoring systems that base on risk factors, debt to income, payment to income and other variables to decide what rates/terms they will offer each person. ive seen people w/ great credit score not get financed and people w/ low credit scores get financed.

When getting a rental, do they check credit history from all 3 bureau or only 1?

We recently got a rental that we will move in this month and they supposedly checked both of us' credit history but I just checked Equifax and there was no inquiry for me in the last 2 years. Do potential landlord/agency check credit history from all 3 or 1 bureau? Out of 3 credit bureaus, which one is most up to date and reliable/accurate?

Everything depends on the landlord, but most only check 1 bureau. While all 3 bureau's have reports all over the country, it seems like each part of the country has a favorite one used by businesses. So, as to which one is most up to date and reliable, they all should be, but one is checked most often in your area.

Which credit bureau does discover and amex. use to check credit for credit card apps?

Both Discover and Amex did credit inquiries on myself through Experian.

Which credit bureau is best for checking your credit?

I know not all companies report to all 3 credit bureaus.

It is best to check all three. Of course not all companies use all three bureaus. But I would want all my credit to be god enough.
Scenario:
You apply for a car loan....they use experian.
You apply for a line of credit....they use equifax.
You apply for a home loan.....they use trans union.

Three different scenarios. Three different companies use three different credit bureaus.
Why just perfect one and not the others?
These are your resources...use them wisely and you will be rewarded.

Do Mortgage lenders check credit scores from all 3 bureaus or do they check from any 1 bureau randomly?

My wife and I will be applying for a home loan soon and between 6 total scores, we have 4 which are above 680 and 2 that are hovering just under 600. Will the lenders take the middle score, an average, or simply select a random score?

The majority of them look at all 3 scores and then consider the middle score to be your score. (middle score per person, not the two middle scores between both you.)

However some lenders DO look at only one. I jsut bought a house through bank of america with more than 20% down and they only pulled experian-- which was a surprise.

Just ask them their policy. It's not a secret.

And if your'e saying you both have 2 high scores and 1 drastically lower one, find out why-- you might need to dispute some info.