I would really like to see all of my questions and answers on the profile page, even if some of them were deleted, and I don't have enough rep to see them on the site.
(Note that some questions are automatically deleted after 30 days or 1 year, and the author might be oblivious about what happened.)
Since February 2020Since February 2020, the "deleted recent [questions/answers]" links in one's own user profile now list all respective posts that were deleted in the past 60 days, rather than just those that were originally posted in the last 60 days.
Since December 2015Since December 2015, users with the "access to moderator tools" privilege (10k+ on designed sites"full sites", 2k+ on sites with beta and non-designed siteslevel reputation thresholds) can use the search operator
deleted:1to see all their own deleted posts.Since June 2013, deleted questions and answers that were posted in the past 60 days, can be seen using the "deleted recent questions" and "deleted recent answers" links on the questions and answers tabs (at the bottom of the tab) in your user profile.
For older posts: as of 2013-04-23 you can view your own deleted questions if you already have a link to them, but they still aren't linked from the user profiles (not even just for you). Nor do you see inbox notifications for comments on them if you come back a few hours later. You have to have thought to bookmark your question, or you have to go digging for it in your browser history.