Yes, there is a feature for marking questions which we like. It is Favorite questions. This feature can be useful in many ways keeping different types of users in mind.
Many users use Stack Exchange for different purposes. Some mark a question as favorite so that they can refer a program which they found helpful, some mark because they liked the description of a question or explanation in an answer very much. Similarly, we can use this feature for marking unanswered questions as a reminder.
We can see a star under every question. This will be saved in your favorites list in your profile.
After favoriting question, it looks in golden yellow indicating it's your favorite question.
You can view those questions based on votes, activity, views and date you have added as favorite. Whenever there is an activity in the posts you have marked as favorite, Favorites tab shows a number to remind us about them.
There is also a search query for searching favorite questions by any user with following format. If user id is 5212 (which is mine) infavorites:5212 gives out the list of questions I favorited.
No questions are removed from favorite list even they are deleted. We can look at them if we have a privilege of access to moderator tools (reputation over 2k).
We can use this feature to add unanswered questions for writing answers later.