Quoting this article with some added emphasis: This excellent introductory article to prose and verse in Shakespeare covers not only the meanings and some examples of each of the three (you're probably already familiar with these terms) but also a nice summary of how each of them tends to be used in Shakespeare's plays specifically.

As a general rule of thumb, blank verse is the standard, while rhyming verse is reserved for more flowery speeches or occasions when it's OK to sound a little unnatural, and prose is used for more down-to-earth talk, often between lower-class people. The types of writing in Shakespeare's plays is usually split into three distinct types: rhyming verse, blank verse, and prose.

There's actually a pretty consistent pattern governing when he used prose and when he used verse, and similarly, when he broke the pattern of iambic pentameter, there was usually a reason for it based on the nature of that particular speech. But when he did use verse, it's usually iambic pentameter, with some exceptions. There's plenty of prose in Shakespeare - indeed, at least one play ( Merry Wives of Windsor) is written almost entirely in prose. In fact, much of the content of Shakespeare's plays isn't even written in verse.