A square can be subdivided into 4 squares, each scaled by a factor of $\frac{1}{2}$.
A right-angled triangle can generally be subdivided into 2 similar triangles of different size.
What other shapes, possibly fractal, of any topological dimension, may be subdivided into finitely or infinitely many similar shapes, at least two of which are scaled by a different factor?
What shapes can be composed of differently scaled copies of themselves, with no intersection?
Most of these kinds of shapes are in the category of "Rep-tiles" (Repeatable tiles). You can read into this Wikipedia article on them if you want. This shows there are many different shapes who can be made up of scaled copies of themselves and they can't easily be put into one list. Those include simple shapes like squares and triangles but also some fractals and other more complex shapes.
But here are a few interesting examples:
Squares.
Shapes made up of multiple squares with the same size which you can create bigger squares out of.
"L-shape", used for the L-substitution.
Triangles.
The same thing but with equilateral triangles (if you can create a big triangle, you can also create the same shape but bigger).
Others.
Fractals.
Dragon Curve:
Elongated Koch Snowflake:
Sierpinski Carpet: