Short answer: I think it is neither ethical nor good (in terms of education, independent of ethics) to force students to use your textbook.

(Assuming that we are talking about a "normal" lecture, as opposed to a workshop about your book.)



Long answer: I see 3 different (but connected) difficulties here. None of them needs to be a problem, but together, they can trap the students. 


requiring a particular textbook: to me this is less of an ethical problem if it doesn't boil down to forcing the students to buy that particular book.
Nevertheless, I think it preferable from an education point of view to teach students that they left the kind of school where exactly one solution exists, and now they are in a world with lots of sensible alternatives. Giving  recommendations* (plural!), IMHO it is a most important point to make that the library holds even more useful books [also on that topic].
more or less forcing students to buy a textbook  


(Recall that the origin of "lecture" is that a (text)book was read to the students. So historically, the lecture was a solution to the problem that books were too expensive for students to buy.)


I don't see why buying the textbook is necessary. Even if book and lecture are (naturally) close. 


  I might assign readings or homework problems from the book, so that the student needs access to the book in order to do them


Why would that be:


Is is that difficult to prepare a slide of the homework problem which is displayed at the end of the lecture or a pdf that can be downloaded?
Reading: I have to say that at university I've never experienced assigned reading from a textbook. So my question to you is: is it really necessary to assign reading chapter 7.4 as opposed to assign preparing the principles of pH electrodes? Also, I've seen reading materials for download.
Making small parts of the book available to the students is probably possible even if the contract with the publisher doesn't let you distribute pdfs to the students. At least, e.g. in Germany, it is even possible to hand small parts from any book (not only yours!) to the class for teaching purposes.
For the self-study aspect of the textbook, there is the textbook collection of the library. The university libraries I know have sensible numbers of the important textbooks to be borrowed by the students plus a number of copies that stay in the library so they are always accessible.  Are the books there really not sufficient? If so, why not? Why are the important books not there? How can books be bought?
(How to get your book into the collection is part of the next point:)

Possible conflict of interest because it is your own textbook.
This is the interesting part. But, if you take care of the first two problems, there is already much less space for an actual conflict of interest (≈ a real problem for the students) here.
Or, taking another point of view, I perceive taking unfair advantage of the position***  as a symptom of (un)ethical behaviour which is closely bound to the whole character. In that I perceive it less of a single problem that is solved or not by a particular line of action on this point but rather a problem that appears with some people and not with others.
In yet other words, people who take advantage of their position tend to do that in more ways than just this (e.g. in the combination of my three points - at which point @JeffE probably recommends to run). The formal action of not requiring their own textbook doesn't help much. Students will conclude from the general reputation/perception of taking unfair advantage that the book is required - whether it is stated openly or not. 


I guess it is one of the topics where those who do worry whether what they do is ethical are the ones who don't need to worry (because they do act ethically) - it would be far more important that those who don't would start to worry...

Whether to donate copies of your own textbook to the library, 
make a donation that reimburses the library for your royalties, or 
convince the library to buy it like any other book, and/or 
whether and how you want to reimburse students 
is IMHO unanswerable as a general question.
I think valid points can be made for and against** each of the options here.

Good and sensible decisions will depend a lot on the particular circumstances and even more on the personality of the professor.



Side note: 


  Or, use my royalty earnings to buy pizza for the class.


I object to this option on the following ethical grounds: If my problem is that I'm too poor to buy textbooks, I don't want to spend money on pizza but would rather like to save that money towards the next textbook. 



* A professor not recommending his own textbook sounds about as convincing to me as a vegetarian running a sausage factory. 

** Here's the advocatus diaboli against each of the points:


Donating books to the library? Someone is buying fame!
Reimbursing the royalties - same as above, but more greedy (or the one above was more desperate for fame...)
Convinced some committee to buy the books? Surely there is a textbook-buying circle emerging: You scratch my back and I'll scratch yours.  
reimbursing students who buy the book: that's an obvious attempt to whitewash the reputation
and so on


*** As long as you do not take advantage of your situation, the conflict of interest is at most your problem (i.e. you are worried). If you take unfair advantage, the students have a problem.

Is it ethical to profit by having my students buy my textbook?
I'm not native in the English language and I'd like to know if when I say "Viewpoints made easy" your perception leads you to something like:


  Viewpoints made easy. An easy form to
  connect and represent points of view
  and understandings about the world
  knowledge.

