What effect does the ending of Mass Effect 2 have on Mass Effect 3?

At the end of Mass Effect 2 you have the option of either

destroying the Collector base or preserving the base to allow Cerberus to study it.

What effect on Mass Effect 3 (if any) does this decision have?

Saving the base gives you 110 points towards your Galaxy at War score compared to 100 for destroying it.

There is a rumour that the Illusive Man will be friendlier towards you in ME3 if you went his way in ME2 (saving the base) but that's unsubstantiated.

Since he's (confirmed) trying to kill you in ME3, I don't know how much weight this carries.

The endings below 1750 or above 2800 effective military strength are the same, regardless of what you chose to do in ME2.

The endings, organized by rating required are different depending on what path you chose:

Low EMS Option

Saved the base:

1750-2049 EMS Choose to Save the Reapers and the Earth will be saved.

Destroyed the base:

1750-1899 EMS Choose to become a Reaper and the Earth will be destroyed.

Mid range EMS Option

Saved the base:

2050-2349 EMS Choose to become a Reaper and the Earth will be saved.

Destroyed the base:

1900-2349 EMS Choose to destroy the Repears and the Earth will be devastated

Saved the base only option

2350-2649 EMS Choose to destroy the Reapers and Earth is destroyed.

High EMS Option

Saved the Base:

2650-2799 EMS Choose to destroy the Repears and the Earth will be devastated

Destroyed the Base:

2350 - 2799 EMS Choose to become a Reaper and the Earth will be saved.

It will slightly increase your galactic readiness to save it.