Is it grammatically correct to say Any updates?

Answer 1

In informal conversational English it's perfectly acceptable -- implied parts of speech are common and usually easily understood from inflection and context (see below). In a formal setting, or to avoid confusion, you should supply the missing part of the sentence. The sentence fragment could -- based on how it is said, to and by whom, and in what context -- mean any number of things, such as: "Do you have any updates for me?" "Would you like me to provide you with an update?" "Do you really want all the updates I have available, or are you after something specific?"