I'd like to have a bunch of Algebra I and II level math exercises for
my kids to work on, with answer keys.  It would be nice to find
something which had lots and lots of problems that I could simply
print out and use.  That way, if the boys need to give more attention
to one area, then we'd have an abundance of material to work on in
that area before going to something else.  Surely, there are some good
websites/materials available along these lines?

Hi jat,

Thank you for an interesting question.  

Math.com - The World of Math Online
http://www.math.com/students/worksheet/algebra_sp.htm

Algebra Worksheet Generator (create answer sheet) - Create up to 900
problems and answers for each category!

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AlgebraHelp.com
http://www.algebrahelp.com/worksheets/index.htm

Worksheet Index - each page has 20 questions - create Answer Sheet

Worksheet Index Basic Equations
Simple problems for those who are just being introduced to equations. 

Basic Proportions
Practice solving basic proportions.

Simplifying and Solving Equations with Multiple Signs
Equations that have more than one sign between terms.

Simplifying and Solving Equations by Combining Like Terms.
You must combine like terms before solving these equations.

Simplifying Multiplication Worksheet.
Practice multiplying two terms (monomials).

Multiplying Using the Distributive Property.
Practice multiplying a term and a parenthesis with more than one term.

Foil Method Practice Problems.
Practice multiplying two parentheses using the FOIL method.

Simplifying Exponents of Numbers.

Simplifying Exponents of Variables.

Simplifying Exponents of Polynomials (parentheses).

Simplifying using the Order of Operations.
Ten Expressions to practice using the Order of Operations. 

Negative Exponents of Numbers

Negative Exponents of Variables

Negative Exponents in Fractions

Factoring Numbers

Finding a Greatest Common Factor (GCF) of Two Numbers

Finding a Greatest Common Factor (GCF) of Two Terms

Factoring a GCF From an Expression

Factoring a Difference Between Two Squares
 
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Kids Math SyvumBook Level II - Algebra
http://www.syvum.com/cgi/online/serve.cgi/kmsl2/kgmat7.tdf

After clicking "Score and Show Answer(s)", click the "Try another set"
button at the bottom to get a new set of questions.

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Math worksheets with solutions!
http://www.clc.mnscu.edu/kschulte/mathworksheets.html#Intro

Click on the links for Intro to Algebra and Intermediate Algebra 

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EdHelper.com - $19.99 USD
http://www.edhelper.com/

edHelper.com - Subscription for Grades 9-12 (includes algebra)   

Select the skills to include:
Equations  Exponents  Linear Equations  Systems of Linear Equations 
Inequalities  Functions  Matrices  Simplify Algebraic Fractions 
Polynomials  Factoring  Polynomial Functions  Radical Numbers 
Advanced Radical Numbers  Quadratic Equations  Conics  
 
(see sample worksheet)
http://www.edhelper.com/Algebra1Test.htm

Answer Key 0518578

Sample - Sample Algebra 1 Review Worksheet
This is only a sample pre-made worksheet. If you were a subscriber,
the answers would appear on the second page that is printed out. Sign
up now for the grade 9-12 materials!

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PurpleMath.com
http://www.purplemath.com/internet.htm

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MathPower.com (no answers that I could find though) 39 Internet assignments
http://www.mathpower.com/mth3hmwk.htm

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AlgebraHelp.com  
http://www.homestead.com/stroh/algebrahelp.html

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Best regards,
tlspiegel

Thanks.  This will get me started.  Stuff is easy to find when you know how, right?