I'd like the now() operator to accept an increment like the other date functions (startOfDay(), endOfWeek(), etc.)

The alternate syntax would be:
now("inc")
where inc is an optional increment of (+/-)nn(y|M|w|d|h|m)

For example, this could allow one to create a scheduled filter to send them new issues matching a specific query every hour:

... affectsVersion = "4.4" and created >= now("-1h")

We were looking for this kind of functionality for users who only want to be notified of new issues matching certain criteria. The notification schemes and component watchers didn't provide the functionality we were looking for.