First, I want to agree with what other people have said: Pull ups, chin ups, dips, squats, and planks are all extremely good bodyweight exercises.
I'm going to suggest a few different ones on top of those.
A few weeks ago, I decided to incorporate some gymnastics moves and exercises into my home workouts. Since some of these moves are extremely difficult, they can be broken down into a set of progressions (and supplementary exercises), which increase in difficulty. I'll include some resources about the specific exercises at the end of my answer. Anyway, these are the exercises that I'm working on right now:
- Planche Progressions (a series of exercises that work you up to a full planche)
- Front Lever Progressions (a series of exercises that work you up to a front lever)
Though my knowledge of gymnastics is very limited, it seems like a recurring concept in gymnastics is that movements can be made much more difficult by decreasing leverage. For example, let's say you're doing a normal push up, so your hands are below your shoulders. Now, scoot forward with your feet (while not moving your arms) so your hands are now in line with your ribs. Try doing the push up again now--it'll be more difficult because you've decreased the "lever arm" of your movement. Try scooting forward so your hands are near your waist and try again...this should be much harder. (This variation of the push up is sometimes referred to as a "pseudo planche push up" and can help strengthen the muscles used in the planche).
So in essence, if you do exercises where you can vary the leverage (like these ones), you have a sequence of exercises of varying intensity. These exercises are also all quite intense to begin with and only get harder. Furthermore, they all will workout your core quite a lot, especially in an isometric manner (i.e. in a static manner like a plank and not a dynamic motion like a sit up), as well as lots of other muscle groups (with the front lever and the planche you have pushing and pulling movements). As a result, these exercises seem to fit your requirements. Also, because of their novelty, I've found them to be really fun.
The front lever will require a pull up bar (hope this is obvious after watching the video), so as other people have mentioned, you should definitely get one if you don't already have one.
If you can't hold the first front lever progression (see resources below), work on lifting your knees to your shoulders (while hanging on a pull up bar).
Parallettes (the low parallel bars) are good to have but I haven't needed to use them yet (I'm not very far on these progressions). Using the seat of two chairs for working L-sits can work. Also, you can build your own set of parallettes using PVC for quite cheap (see "Drills and Skills" in resources), which is what I'm planning to do.
If you're new to these exercises be EXTREMELY CAREFUL. Some of these exercises put a lot of load on your wrists and shoulders, so always make sure to properly warm them up beforehand.
Once again, I'm not a professional gymnast, and this is information that I've gathered myself by researching online. If there gymnasts reading this, maybe they can add some additional tips, pointers, and resources.
Links and Resources
First, you should read this article, which inspired me to use these exercises in the first place. This article details the basic progressions that you should work on for both the planche and the front lever while providing a much more thorough motivation of why these are good exercises to do.
Youtube Videos: Here are some videos that I've found to be helpful, especially the front lever tutorial, which is very thorough.Front lever tutorial, L-sit tutorial
Drills and Skills - A website about general gymnastics information that's really useful, including how to build your own parallettes.