What can I do to minimize my Skyrim save game size?

For PC players, install the Unofficial Skyrim Patch. Among its fixes are (emphasis mine):

• NPCs will no longer drop weapons or shields as separate objects, as these are never cleaned up which greatly adds to save bloating and litters the gameworld (the items will still appear to be dropped, but will access the corpse's inventory to be taken and be cleaned up with the corpse if left).
• Ghostly Remains, Ice Piles and Wisp Cores will no longer permanently remain and bloat the save file (they will either disappear on exit of the cell or when the cell resets).
• Civil war map flags are not displaying properly. This is due to a bug in CWMapActivatorScript which does not clean up placed flag activators. The fix also removes bloat from excess flags that have been accumulating. It will be necessary to visit each affected map twice before the cleanup can take effect on existing saves though.

Note that the official patches have now fixed ash piles and nirnroots not being properly cleaned up.

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Another option to fix already bloated save game files is by using Skyrim Script Extender's (SKSE) ClearInvalidRegistrations console command.

As per SKSE's v1.6.7 changelog:

add console command ClearInvalidRegistrations to remove invalid OnUpdate() registrations

This prevents orphaned OnUpdate() events and the resulting bloated/broken saves when removing certain mods. When applied to an already bloated save, it will stop growing further and instead shrink over time as the game processes all queued events. This may take hours depending on the amount of bloat.

To execute automatically after each reload, add this to \Data\SKSE\skse.ini:

[General]  
ClearInvalidRegistrations=1

Related forum discussions about this SKSE feature:

• Skyrim Nexus Forums, "How to CLEAN your SAVEGAMES from BROKEN SCRIPTS"
• Bethesda Forums, "Skyrim Script Extender (SKSE)"

The best thing you can do is minimize your interaction with objects, esp trash objects. Skyrim has to track the position of every cup you knock off the table, so the more you disturb the "natural" world, the bigger your save file becomes.

You can also allow time to pass (as you mentioned), turn off or reduce the number of autosaves, and keep 2GB of free space on your hard drive.

See also: Tips to Reduce Skyrim Lag

Edit: It seems the PS3 has a safe mode feature that may also help; it's linked in the 2GB free space link.

This is what works for me, but it is a SLOW process!

What I have been doing is going back to old locations (starting with Helgen), and stealing EVERYTHING. clear old areas out of all loose items! Then I sell it.

I think it removes those loose items from the game entirely. So far, I have gone through Helgen, Bleak Falls Barrow, and stolen everything loose from Riverwood.

I have gone from a 37meg save file, to a 18.9 meg save file. Game runs a lot better, freezes are happening far less.

Just note, make sure you know where there is a fence to sell your stolen things.