Games where bases can be attacked?

Zero Wing

State of Decay - Lifeline Expansion

matches all things what you are asking for: home base will be attacked at random whenever too many zeds are in the area and it's open world.

State of Decay I think, while you go out for resources, your base could be attacked by a horde of zombies. Don't quote me on that, I haven't played it yet (but I've read about it)

GTA San Andreas :D

In GTA: San Andreas your territories randomly get attacked by enemy gangs. However, this is only around the start and end of the game.

The Saints Row games (have only played 1 & 2) do have gang attacks, probably similar to the ones mentioned from GTA:SA

Once you completely take over territory, there won't be any more attacks though..

Also, haven't played them, but I thinkI've read that the original XCOM games had occasional alien attacks against your base..

Assassin's Creed: Revelations.

There was Jagged Alliance 2. That wasn't an open sandbox world quite like you're describing, but did involve overworld navigation and having to decide your plans of attack / movement. Enemy forces would often attempt to retake areas you cleared, and if it happened to be populated with a militia you trained, you would have to defend (either with an auto-resolve, or by actually taking part with a PC member).

Obviously not what you are looking for, but just based on the title alone, Dota 2 comes to my mind. Your base could be under attack at random times while you are pushing. :p

Tycoon and survival crossbreed genre games like Dwarf Fortress (Castle Story, Timber & Stone for example) although you won't be traveling around the world on your own.

I think something like Mount and blade.

I think something like Mount and blade.

Well, there is a similiar game to State of Decay where your objective is to defend your base. It's called Fort Zombie. It's pretty bad though.