The best program to design books would be Adobe InDesign, as this program was specifically created to design multipage files intended to be bound in some fashion and has several useful features.
These include:
Facing Pages: This setting arranges the pages in "Reading View", where the front and back covers are by themselves and the rest of the pages are displayed in pairs, the way they would be when the book is printed and bound. This is especially helpful for artwork that requires "Cross-Overs" or pictures and/or design elements that cross over the spine from one page to the page next to it.
Master Pages: This feature allows the designer to set up elements that appear on all or several pages. Things like headers, footers, page numbers, etc can be designed on the "Master" page, and the master applied to other pages so that they will be the same location throughout the entire file
Layers: This is very useful when designing publications that have several versions, but the majority of the content is the same. For example, a product catalog where all the product descriptions, images, etc are the same but there is different pricing for Canada, The United States, and Europe. The whole catalog can be designed in one file, and the different prices placed on 3 different layers that can be shown or hidden depending on which version is being exported. This eliminates the need to maintain multiple files for the same publication and makes sure that all of the content is the same across all variations
Export PDF Settings: InDesign comes with several PDF export profiles built-in, including one for Print-Ready Output. These settings can be modified and custom profiles created, but for those who are not familiar with these options, the default will work for most, if not all, print applications
Integration with Illustrator and Photoshop: Because all three programs are made by the same company, they were designed to work together. Photoshop or Vector (.ai or .eps) files can be inserted as "Smart Objects", which means any time those files are edited with either Photoshop or Illustrator and saved, the Smart Object is automatically updated. As well, the Smart Object can be opened into the editing application from InDesign through the Smart Object interface.
Margins and Columns: These features allow the designer to define the margins around the edges of each page, as well as the number, width, and gap between columns. This makes it much easier to arrange elements such as text and images in a consistent manner.
If InDesign is not available, other programs like Illustrator, Photoshop, Word, CorrelDraw, etc can be used, the only requirement for the design program being used is that it can export a PDF file. However, most other programs, unless they are also designed specifically to create multipage bound files, will not have the same features as InDesign.