Formal:
* Diatribe: A bitter and abusive speech.
* Harangue: A lengthy and aggressive speech.
* Tirade: A long, angry speech.
* Invective: Abusive or venomous language.
* Philippic: A bitter verbal attack.
Informal:
* Rave: To talk excitedly or incoherently.
* Spout: To speak rapidly and at length.
* Vent: To express strong emotions, often in a negative way.
* Go on and on: To talk excessively.
* Let off steam: To release anger or frustration.
* Blow off steam: Similar to "let off steam."
* Give someone a piece of your mind: To express your anger or displeasure directly to someone.
* Lay into someone: To criticize someone harshly.
More neutral:
* Expound: To explain or discuss something in detail.
* Declaim: To speak in a loud and forceful way.
* Orate: To speak in a formal or eloquent manner.
The best synonym for "rant" will depend on the specific situation and the tone you want to convey.