More and more commonly, I find that websites elect to hide or remove the submit button from forms. One obvious example is this site (along with other StackExchange sites), whose search field lacks a button labeled "Search" or "Go".
As a user who rarely uses his mouse to fill out forms, this isn't an issue for me. In fact, I often prefer the cleaner look of search forms without it. However, I imagine that it might cause confusion for certain types of users (e.g. those who click the "Google Search" button instead of pressing enter).
My sense is that this becomes more and more problematic as the number of fields increases. For example, a login form with two fields might occasionally do without the submit button, but a registration form with ten fields probably shouldn't.
Can someone point me to any research to back up or debunk my claim? Or for those of you that skipped the first three paragraphs of my question, how is usability affected by removing the submit button from various types of forms?