This topic is actually surprisingly complex. There are lots of different ways time zones can come into play.
Manual Reports
You manually run a report by opening it up, and clicking the Submit button.
If your report has logical dates selected like Last Month, This Week, or Today - then those are translated into real dates. The user's time zone is used to convert the logical dates into real dates. For example, if your report is set for "Today", then "Today" is defined by the current time in their time zone.
A user's time zone is set on their user profile. By default, it is the same as their installation's time zone, but it can be changed.
Scheduled Reports
Scheduled reports are run automatically according to their schedule. The schedule can be viewed or edited by opening the report and going to the Scheduling tab.
When a scheduled report is saved, we also save the user's time zone with it. A user's time zone can be found on their user profile. The report will run on a set schedule based on that saved time zone. For example, if the report runs every day at 3pm, then it will run at 3pm in the saved time zone.
Reports saved prior to 2011 do not have saved time zones. These run according to the user's current time zone. That means if the user switched time zones, the report would run according to the new time zone, not the old one.
Date Fields in Reports
What about dates that are returned by your reports? For example, when a user enters 8 hours worked on Tuesday the 25th, are time zones considered? Or, if you run an audit trail report and it shows something changed at 3pm, whose time zone is that in?