One's own convenience or doing things one's own way; selfishness. (Often used as 勝手な to mean self-centered or inconsiderate.)
彼はいつも勝手なことばかり言う。
He always says whatever he wants (is selfish).
勝手に決めないでください。
Please don't decide things on your own.
そんな勝手な行動は許されない。
Such selfish behavior is unacceptable.
How things are done; the surrounding circumstances or environment (e.g., expressions like '勝手がわかる' or '勝手が違う').
新しい職場の勝手がまだ分からない。
I still don't understand how things are done at the new workplace.
この機械は以前のと勝手が違うので、操作を教えてください。
This machine works differently from the previous one, so please teach me how to operate it.
Convenience or ease of use; how suitable or handy something is to use.
このソフトは勝手がいいので、すぐに使いこなせた。
This software is easy to use, so I mastered it quickly.
勝手のいいデザインに変更した。
We changed it to a more user-friendly design.
Financial circumstances or livelihood; one's condition or means of living (somewhat older usage).
今の勝手では子どもを大学に行かせられない。
With our current financial situation, we can't send our child to university.
The kitchen (i.e., the area for cooking) — used to refer to the kitchen or its vicinity.
勝手口からゴミを出してください。
Please take the garbage out through the kitchen door.
台風で勝手口のドアが壊れた。
The kitchen door was damaged in the typhoon.
In archery contexts, a technical term referring to the hand that draws the bowstring (often the right hand).
弓道では左手で弓を持ち、右手（勝手）で弦を引く。
In kyudo, you hold the bow with the left hand and draw the string with the right hand (called 'katte').
Used as a prefix to indicate something unofficial or unauthorized (e.g., 勝手サイト = an unofficial website).
これは勝手サイトなので、公式情報とは限らない。
This is an unofficial site, so it may not contain official information.
スマホに勝手アプリがインストールされていた。
An unauthorized app had been installed on my phone.