Why are "word suggestions" of keyboards not shown in some apps? I'm using Hacker's and SwiftKey X keyboard on GingerBread. Suggestion line is shown in most apps above the keyboard. But when opening the keyboard in Android Market (now Play Store) or DroidEdit (code editor), the suggestions aren't shown for any keyboard I use.

What determines this behaviour? How can I switch on/force suggesting words?
Most likely the app has chosen not to show them for that particular input box. From a technical perspective, this is controlled by flags on the TextView object that represents the text area control (e.g. the TYPE_TEXT_FLAG_NO_SUGGESTIONS option). I don't believe there is any way to override this setting if the app chooses to disable it.

It's probably also important to note that it's a bit of a one-way street. Suggestions are enabled by default on all text areas, but will obey the global setting, so an app can't forcibly enable suggestions in any way. If you have the global setting turned off, they're off everywhere.

The logic that the developer documentation provides for allowing apps to forcibly disable suggestions is that in some cases they simply aren't very useful. The specific relevant quote would be (from the above link): 


  ... This is useful for text views that do not contain words from the language and do not benefit from any dictionary-based completions or corrections ...


I'd wager the Market disables them because app names and such have no obligation to be dictionary words, so suggestion attempts would often prove rather futile. I would also understand the same being true of your second example, which sounds like a source code editor (I assume that's what you mean by "syntax highlighting"). It would be sort of akin to Visual Studio underlining misspelt words in source code - it provides no benefit since most of the text will not be dictionary words.