Here are some examples:
* For contrast:
* However: "The cat was hungry, *however*, it didn't want to eat the food."
* Nevertheless: "She studied hard, *nevertheless*, she failed the exam."
* Yet: "He tried to be quiet, *yet* he still woke the baby."
* For exceptions:
* Except: "He loves all animals *except* cats."
* Besides: "They liked everything *besides* the dessert."
* For adding something contrary:
* Although: "He is a talented musician, *although* he doesn't have any formal training."
* Despite: "She went to the party *despite* feeling sick."
* For expressing a consequence:
* Therefore: "It was raining heavily, *therefore* the game was cancelled."
* So: "He was tired, *so* he went to bed early."
The best word or phrase to use will depend on the specific situation.