Book recommendations from basic algebra to precalculus? I graduated high school a while ago, hardly remember anything and have no idea where to begin relearning. 
 A: I highly recommend A Course of Pure Mathematics by G. H. Hardy for when you feel you have re-acquainted with high school mathematics. This one is written for those ambitious first year university students who have no prior analysis exposure but have the zeal to learn the details which high school calculus exposure just omitted because it might hurt majority pupil's head and put them off mathematics for good.
A: I think that Courant and Robbins What is Mathematics? is a very good introductory book yet. It is worth reading and I have spent some time on it before starting my undergraduate studies. The title is not reflecting the real content of the book.
A: It depends how good you want to be at mathematics. In any case, Problem Solving Strategies by Pólya is an excellent place to regain one's footing. From there I would perhaps look at some of the books in the Art of Problem Solving series (www.ArtofProblemSolving.com; There are forums on this website on which it would be more appropriate to ask the type of questions that you are likely to run into.) Then perhaps you could move on to The Art and Craft of Problem Solving to round things off after finishing up calculus. More resources include: Khan Academy, The Online Math Circle, www.cuttheknot.com, and try searching for videos done by a person named Vi Hart if you are looking for inspiration. But this is all overkill if you just want a basic grasp of high school mathematics.
A: If you have the patience and you really want to learn, I'd recommend you check out Khan Academy. His videos are very easy to understand and if you like watching his video, as far as you are concerned, you can go beyond what you'd normally be expected to know. 
You can get yourself ready for college by watching his calculus playlist (SV to MV Calculus covered) or his Linear Algebra Playlist. 

I can go on forever about how great it is, especially for curious High school students (It really doesn't cover things beyond Calculus or Elementary Linear Algebra but still, it is good place to start.)
Edit: If the OP prefers books to video lectures then I'd say that he try the Schaum's Series or Bob Millers Math For the Clueless Series. I can only think of good books for problem solving strategies (Like Polya's "How to Solve it" or Krantz "Techniques in Problem Solving") but if you want books on high school material, I guess this is one way to go.
Edit 2: In one of the newer answers, there has been a mention of "What is Mathematics" by Richard Courant and Herbert Robbins. It is a very good book and it touches from simple concepts of the Number System to some Geometry to fairly advanced topics in Mathematics like Theoretical Calculus (Analysis) and General Topology. It has all you require for High School and if you like it it gives you a very nice basis to move forward. There is no harm knowing something about Neighborhoods or Connectivity of objects, is there?
 I Hope it Helps
A: For an introduction to set theory (to prove things like the associative property of addition), I recommend: 
Classic Set Theory for Guided Independent Study
http://www.amazon.com/Classic-Theory-Independent-Chapman-Mathematics/dp/0412606100
A: Schaum's Outlines are excellent for you.  Simple words, lots of problems.  Not covered in tons of random pictures and complicated explication (more directed to textbook selection committees than to using students!)
I disagree with Hardy recommendation for an older student who probably did not achieve mastery the first time (given he is asking for help here).  Hardy is a book that a lot of bright kids and teachers enjoy with neat things to recommend it. But is not a down to earth review, not most suited to this person pedagogically.
