General time references:
* Day by day: Describing a gradual process.
* Day in, day out: Something that happens regularly.
* From day to day: Living without long-term plans.
* Day after day: Emphasizing the repetitive nature of something.
* To this day: Meaning "until now".
* One day: Describing a future event.
* All day long: Throughout the entire day.
* At the end of the day: Ultimately.
* For a day: For a short period of time.
* Days gone by: The past.
* Day of reckoning: A time when people will be judged for their actions.
* Day of the week: A specific day like Monday, Tuesday, etc.
Specific events:
* Birthday: A day to celebrate the anniversary of someone's birth.
* Wedding day: The day of a wedding ceremony.
* Game day: The day of a sports event.
* Opening day: The first day of a season or event.
* Election day: The day when people vote.
Figurative uses:
* Bad hair day: A day when one's hair is particularly unruly.
* Lucky day: A day when good things happen.
* Black day: A day of tragedy or disaster.
* Name your day: To be able to choose a specific day for something.
This is just a small sample. There are many other phrases containing the word "day". You can also use the word "day" to describe specific days of the week, holidays, or events.