Anyone who thinks "Alg II is for everyone" should learn some basic statistics.

Source: Requiring Algebra II in high school gains momentum nationwide Washington Post

As a mathematics teacher, this particular issues touched a nerve.

Confusing "correlation" and "causation" is one of the most common errors in all statistics.

These two quotes from the article:

(1) [..] whether learning Algebra II causes students to fare better in life, or whether it is merely correlated with them doing better — because smart, motivated kids take Algebra II — isn’t clear. 

and

 (2) Among the skeptics is Carnevale, one of the researchers who reported the link between Algebra II and good jobs. He warns against thinking of Algebra II as a cause of students getting good jobs merely because it is correlated with success.
“The causal relationship is very, very weak,” he said. “Most people don’t use Algebra II in college, let alone in real life. The state governments need to be careful with this.”

state it very nicely.

xkcd

Here is an example of confusing correlation with causation.  Everyone knows that all heavyweight boxing champions are big, strong, fast, and have boxing skills. In other words, being a heavyweight champion is strongly correlated with being big, strong, fast, and having boxing skills.  This doesn't mean that being big, strong, fast, and having boxing skills causes one to become a heavyweight champion! Sure, it can help, but it is by no means a cause.

The individual must train hard their entire lives, must show extreme dedication and passion for the sport, and usually possess something "special", a strong will, a never-give-up attitude, etc. -- intangibles which are in no  way related to being big, strong, fast, or having boxing skills.  (there are paraplegics who have strong wills and never-give-up attitudes, for examples)

The danger, [Carnevale] said, is leaving some kids behind by “getting locked into a one-size-fits-all curriculum.”

This point is 100% valid.  Students develop at different rates, and those placed in a track which is no longer appropriate for them should be able to move to one which is more appropriate.  Schools should offer algebra II for those students who are ready and willing to take it on.  If there are to few students, hopefully the school will have access to the internet so their students can use a tool like Khanacademy to learn at their own pace.

What math topics should "every student" know before they graduate high school?  

Here is a short list I cooked up, feel free to add your own thoughts in the comments.

• Arithmetic with positive and negative numbers -- in other words:  how to balance a checkbook
• Elementary propositional logic, specifically that the converse of a statement is not always true.
• Proportional reasoning, specifically "A small percentage of a large quantity can be large" and "A large percentage of a small quantity can be small." as well as "taking a percentage of a percent." -- "The retirement plan will match 10% of up to 3% of your base salary..." 
• Linear vs. Log scale
• Probability, specifically conditional probability and the normal distribution
• Statistics, specifically the importance of sample space and size, as well as the difference between correlation and causation!
• Be able to read a (well-made) graph or chart which includes any of the above concepts