Question: I've tried researching this question myself, but the only data I can find is over huge timescales, like situations where the continents have reformed back into a Neo-Pangea.

I'm not looking for any real drastic changes in positioning, just relatively minor things like seas disappearing or continents slightly shrinking or pushing into each other. 

Would there be any noteworthy changes at all, or would it be pretty much the same as today aside from some minor changes that wouldn't affect anything?

Let's just assume humanity suddenly stopped existing today for the purposes of the question, so they don't make any more changes to the world than they already have.

As always, I'm very grateful for any answers, and if you need anything clarified feel free to leave a comment and I'll do my best to clear things up.

Answer: 
You mention plate tectonics as a cause of change; there are others

* **Rising sea levels**. [Wikipedia has a map](https://en.wikipedia.org/wiki/Sea_level_rise#/media/File:6m_Sea_Level_Rise.jpg) from NASA about how a 6-meter sea level rise would change the world map. Current predictions seem to be something between 0.3m and 2.5m in the next hundred years, so 6m doesn't seem crazy over 1000 years.
* **Coastal erosion** can cause significant changes: for example, the [seashore at Hemsby](http://www.bbc.co.uk/news/uk-england-norfolk-43472150) in eastern England is receding at the rate of about 35 metres (115 ft) per year.
* [**Post-glacial rebound**](https://en.wikipedia.org/wiki/Post-glacial_rebound). During the ice age, ice-covered land was weighted down; it's slowly springing back. For example, much of Finland was underwater a few thousand years ago, even though sea levels were much lower. Southern England is pivoting downwards as Scotland rises, which will lower southern England by about 0.5m in the next thousand years.
* **Vulcanism** can and does create new islands.
* **Deposition** from rivers causes estuaries to grow out into the sea.
"Is removing people sufficient to stop global warming?" Good question. Answer is not clear. If we have passed the tipping point for arctic permafrost collapse, arctic ocean being ice free in summer, then we may release huge amounts of methane clathrates.

On top of this while oil has to be pumped, natural gas is often under pressure. As distribuiton systems break down, more methane is released.

Net result: ALL of antarctica and Greenland melt over the space of that thousand years.

So we have an new continent free from ice in the south, we have a new archipelago of islands where Greenland was. We have new ecologies in the arctic regions, and the ocean shoreline moves in a bunch.

Details here: <https://www.nationalgeographic.com/magazine/2013/09/rising-seas-ice-melt-new-shoreline-maps/#/07-ice-melt-antarctica.jpg>