When I proof my ebook in ADE, I'm seeing certain long words at the end of a line being split and hyphenated between two lines.

For example, if the word serendipity was at the end of a line on the page, it would look like this:

blah blah blah seren-
dipity blah blah

Is there a command that I can put in the stylesheet to keep my words together and have the entire word drop to the next line instead, like this:

blah blah blah
serendipity blah

These:

hyphens: none;
-webkit-hyphens: none ! important;
-moz-hyphens: none;
adobe-hyphenate: none;

And if you want to be really paranoid:

-o-hyphens: none;
-ms-hyphens: none;

Or disable full justification.

It is generally a good idea to add some of those to chapter titles and similar elements. At the very least, I'd add:

hyphens: none; (CSS3 code, should work with ePub 3 books ?)
adobe-hyphenate; (Adobe-specific, works with most ebook readers)

others are probably more specific to certain readers. Hopefully, browser-based readers will support (maybe in some future) the CSS3 way in addition to their own codes...

It is generally a good idea to add some of those to chapter titles and similar elements. At the very least, I'd add:

hyphens: none; (CSS3 code, should work with ePub 3 books ?)
adobe-hyphenate; (Adobe-specific, works with most ebook readers)

others are probably more specific to certain readers. Hopefully, browser-based readers will support (maybe in some future) the CSS3 way in addition to their own codes...

I definitely would recommend the webkit variant, at a minimum, because iBooks supports it, but at least as of iOS 6, WebKit doesn't yet support the non-vendor-prefixed hyphens property, so unless iBooks is doing some magic, it probably doesn't, either. :)

When I proof my ebook in ADE, I'm seeing certain long words at the end of a line being split and hyphenated between two lines.

For example, if the word serendipity was at the end of a line on the page, it would look like this:

blah blah blah seren-
dipity blah blah

Is there a command that I can put in the stylesheet to keep my words together and have the entire word drop to the next line instead, like this:

blah blah blah
serendipity blah

I would recommend turning off hyphens for things like chapter headers. But do you really want to turn of hyphens in the main body text and cause more gaps?