Ways of saying that a thought came into your mind

Come to
If a thought or an idea comes to you ,you suddenly remember or start to think about it.

- I can't remember his name, it'll come to me in a minute.
- The answer came to me just before the noon.
- It came to me suddenly that what was wrong was that I was tired.

Occur to
If a thought or an idea occurs to you,you suddenly think of it or realize it.

- The same idea had occurred to me.
- I suppose it never occurred to you to ask the police for help.
- It never ever occurred to us that she hadn't been invited.

Enter some ones mind/Cross some one 's mind
If an idea, thought, etc enter or cross your mind, you start to think of it.

- It never crossed to my mind that she may be sick.
- It never entered my mind that I may miss him one day.
-" You could fly to Boston to visit him" ." The thought has never crossed my mind."(used to tell someone you have thought of the thing they are suggesting.)

Strike
If a thought or idea strikes you, it comes into your mind.

- At this point it struck me that I hadn't talked with him for months.
- It's just struck me that I still owe you for the concert tickets.
- A thought struck her.Was she jealous of her mother,then?

Comes/Springs/Leaps to mind
The three expressions mean the same thing :When something comes/springs/leaps to your mind you think of it without making any effort.
Spring to mind and leap to mind show a quickness and suddenness state,however,come to mind is neutral .Come to mind and spring to mind are more commonly used than leap to mind.
Notice that the two latter,usually come with adverbs such as immediately,suddenly and etc.

- Have you any suggestions? Nothing immediately springs to mind.
- As I read the letter a number of things came to my mind.
- When Watching the T.V,immediately the idea sprung to mind.
- Henry asked the first question that came to mind.

- To describe this hotel ,the word that comes to mind is luxurious .
- When he started singing,all my problems suddenly leaped to my mind.

Present itself
A formal expression. If a thought or question present itself to you, you think of it without deliberately trying to think of anything:

- Why not lie about it, the idea presented itself as a perfect solution.
- To escape from the prison was the best idea which presented itself to the prisoners.
- A new thought presented itself to her, that she must kill him.