It does, but like some other English inflectional patterns the syntax is mostly vestigial.

All I ask is that the two of you be polite to each other has be in subjunctive mood; if it were indicative, it would be are instead.

Something that I find interesting is that, while conjugating verbs for mood is largely vestigial in English, the more general phenomenon of paying close attention to the relationship between the sentence and reality, the focus that mood expresses, is very much alive. It's just that it's mostly moved out of the inflectional system.

Mood denotes the informations factuality, if something is, could be, would be, certainly is so, or there may be moods for direct or indirect commands (tell him to come) and so on.

Evidentiality denotes how the speaker knows - you use different evidentiality if you have directly seen something, if somebody told you, or if you deduced it.

Then there is mirativity, which denotes how expected or unexpecred the information was.

I believe that turkish has all tree.