• 書斎しょさい — study; private reading room
• 斎場さいじょう — funeral hall
• 斎戒さいかい — purification and abstinence (before a ritual)
• 潔斎けっさい — ritual purification; cleansing oneself
• 斎藤さいとう — Saitō (common surname)

斎 is strongly tied to the idea of purifying oneself and abstaining before something important. The character is historically connected to ritual contexts (often associated with the idea behind 示), and also links to 斉 as a related form. That is why you see it in words like 斎戒 and 潔斎. Later, it also appears in a calmer, everyday sense in 書斎 — a quiet place to study.