I've done a post like this a few years back, but today I refined the process I obtained the data with and I can present a much better result.

If you're lacking inspiration and don't know what to build, you came to the right place.

This is a file containing pretty much every single aircraft mentioned on Wikipedia, most of which don't even have a page written about them.

EDIT: the file is not perfect, due to the crude way I generated it, there are probably a few non-aircraft entries, most likely short descriptions or notes added by Wikipedia

This is an online tool that you can paste text in, and it'll select a random line.

I'm sure that at this point you know exactly what to do. If not, here's a quick rundown;

Open the text file and copy its entire contents (it may stress your RAM a bit, so don't do this if you have any games or large software running).
Then go to the web tool and paste all the contents in the input box.
Click "Pick a random line" and give the website a few seconds to recover from the immense data overload that you just gave it.
Once it's done, it'll provide you with a random aircraft from the list.

The list itself consists of aircraft, rotorcraft, and gliders. It does not contain every single plane ever built, but I'm pretty confident that it encompasses over 80% of all aircraft ever (with the exception of pre-1914 designs).

If for some reason you can't go through the process I just described but you still need some ideas, I went ahead and pre-generated a few;

Tachikawa Ki-72
Schweizer SGC 6-14
Fletcher PQ-11
Glasflügel 401 Kestrel
Convair F2Y Sea Dart ( <- this one's cool I'm making it lol)
Lioré et Olivier LeO H-23
Lonek L-8 Ginette
Akaflieg Stuttgart fs29 TF