There's never a lack of books to use for learning Python. I occasionally receive books for review, but I don't have a particularly good yardstick to judge such books by: I find that they all contain some factual errors and some oddities of presentation, but I have no idea whether those matter for the readers. Even Knuth's books are full of errors: for example the errata for Vol. 1 (2nd ed.) are a staggering 80 pages, but I doubt anybody besides Knuth himself is bothered by this knowledge.
Recently I got a review copy of "Hello World", and a colleague kindly lent me his copy of "Practical Programming". I think it's interesting to compare the two a bit, since they both claim to be teaching Python programming to people who haven't programmed before. And yet their audiences are totally different!
"Hello World", published by Manning, is written by Warren Sande and his son Carter. The subtitle is "Computer programming for kids and other beginners", but I think if you're not a kid any more you might get annoyed by the rather popular writing style. If you are a kid, well, you will probably enjoy a book written with you in mind, and you will learn plenty. The only prerequisites are reading and typing skills, a computer that wasn't built in the stone age, and a desire to learn more about what goes on inside that computer. The book uses short chapters with lots of illustrations, often cartoons and jokes. There are lots of opportunities to try out the material and learn that way. Each chapter ends with a review section, some tests, and more experiments to try. The book pays plenty of attention to typical "gotchas", so that if you get stuck at some point, there probably is help nearby to get you unstuck.
"Practical Programming" is written by Jennifer Campbell, Paul Gries, Jason Montojo, and Greg Wilson. This a team composed of three university professors and a former student of theirs. Their purported goal is to teach Computer Science (with Capital Letters), and Python is merely a teaching vehicle. But they spend about half of the book on Python itself, covering roughly the same material as any introduction to Python, including "Hello World". Their intended audience is clearly more mature than that of the Sandes, and I would think that Carter Sande and his friends would have a hard time staying focused on the material as presented by Campbell et al. -- their illustrations and diagrams are more functional but a lot less fun.
Both books present a number of projects and running examples. Again, the difference in audience makes it likely that if you love one, you'll hate the other, and vice versa. "Hello World" uses examples from computer games. The games are extremely simple though: modern computer games are some of the most complex system around, and you can't expect to approach them using PyGame and a couple hundred lines of Python. "Practical Programming" takes its example from scientific data processing with an environmental touch: for example, a numerical series is presented as whale sightings over the years and 2-dimensional data is taken from deforestation data. No doubt this is done in an attempt to appeal to a certain kind of student, though the number of potential applications is so large that some students might just as well be turned off by the specific set of choices.
In the end, "Hello World" will leave the reader with a fair amount of practical Python experience, enough to get them started on the long road to becoming a programmer if they are so inclined, or at least enough to give them some idea of what it is that programmers do. "Practical Programming" tries to go further: it presents some well-known algorithms (there's even a discussion of MergeSort), and it has introductory chapters on topics like object-oriented programming and databases. The overall focus is still on being able to use all this new knowledge in one's professional life, and I hesitate to agree with the authors' apparent view that it teaches "Computer Science". Calling it "Computer Use" would cover the contents better, I think, and that's more in line with the series title as well ("The Pragmatic Programmers", also the publisher).
So, how do you learn about Computer Science? Some would no doubt recommend "Structure and Interpretation of Computer Programs" by Abelson and Sussman here. (Someone sent me review copy of that book too.) But really, SICP (as it is often referred to) has its own agenda: convincing the reader that the most important thing computers can do is interpreting computer programs. This agenda has arguably caused the proliferation of Scheme implementations and indoctrinated many young minds with certain ideas about how to design and implement programming languages. But personally, I recommend you go straight to the source. After all these years, there is still no substitute for Knuth.
[UPDATE: fixed book titles as commenters pointed out my typos.]