ExifTool is my go-to tool for time-shifting photos.

Assuming Windows, to add 1 hour to all date/time fields stored in the photo metadata:

exiftool.exe -AllDates+=1 C:\path\to\folder\of\photos

or to subtract one hour:

exiftool.exe -AllDates-=1 C:\path\to\folder\of\photos

By default, this will make a copy of the original as backup before modification. To do the modification in place, use the flag -overwrite_original_in_place:

exiftool.exe -AllDates-=1 -overwrite_original_in_place C:\path\to\folder\of\photos

You can use exiftool to move and rename files based on date/time. To organize photos into nested folders "Year/Month/Day/" with each photo named "image_HourMinuteSecond.[ext]" where the file will maintain its original extension (i.e., JPGs will stay JPGs, DNGs will stay DNGs):

exiftool.exe -d C:/path/to/put/organized/photos/%Y/%m/%d/image_%H%M%S.%%e "-filename<createdate" C:/path/to/folder/of/photos

Note that exiftool doesn't care which direction slashes you use for directories.

For more details about file moving/renaming see this documentation.

ExifTool has options for "dry-running" things, but I often end up zipping up a folder or copying it first before running my commands that rename/move files to make recovery easy just in case it doesn't do quite what I intended.

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Additional usage:

Some of these examples are my own, while some come directly from the exiftool documentation reproduced here for convenience.

Fine-grained date/time adjustment. This is the long form to subtract 1 hour, for which the above is a shortcut:

exiftool.exe "-AllDates-=0:0:0 1:0:0" C:\path\to\folder\of\photos

So, To add 5 years, 10 months, 2 days, 10 hours, 48 minutes, and 4 seconds:

exiftool.exe "-AllDates+=5:10:2 10:48:4" C:\path\to\folder\of\photos

Filter by date/time before adjusting. I use this to fix a missed DST adjustment within a large group of pictures, it filters out anything before the time-shift:

exiftool.exe -if '$createdate gt "2012:03:11"' -AllDates+=1 -overwrite_original_in_place C:\path\to\folder\of\photos

You can run the tool recursively, meaning it will repeatedly go in to all subdirectories of the given path:

exiftool.exe -r C:\path\to\folder\of\photos -AllDates+=1

You can filter by file extension if you want to fix DNGs, but not JPGs, for example:

exiftool.exe -ext dng -AllDates+=1 C:\path\to\folder\of\photos

You can combine all these. Recursively find all JPGs created after Mar 11, 2012 and add 1 hour to the all dates by modifying the files in place:

exiftool.exe -r C:\path\to\folder\of\photos -ext jpg -if '$createdate gt "2012:03:11"' -alldates+=1 -overwrite_original_in_place