Almost all of our reports are date ranges based on last quarter and last quarter-to-date. I spend tons of clicks changing date ranges on reports (and sometimes make mistakes that are hard to spot. This would be similar "Last Period" or "Last Year" which currently exists. It can get pretty fustrating having to manually change all those dates!
Relative dates rarely works for this need. For example, it doesn't work on reports that are not column based (Project activity summary, general ledger detail, etc.). Right now, I have to open up each report to confirm the date range is correct before runing it. A "last quarter" and "last quarter to date" options would allow me to run many/most of my reports without having to open, analyze the settings, modify the date range, save, close, then run.
I also like the idea of running certain reports automatically to a file, but wouldn't be able to do this for my reports without this functionality.