Games that are similar to Time Pilot / '84

[MOSQUITO FIGHTER]

Any recommendations? The only ones that I can think of are Boscanian and Thunder Force II. But they both lack lack amount of directions that you can shoot in compared to Time Pilot. I like how Time Pilot plays and controls, but it's pretty easy.

[Icarus]

If you have an OSX/iOS device, Llamasoft's Five A Day is very very good.
http://minotaurproject.co.uk/Minotaur/fiveaday.php
I've played it to death and it's really enjoyable and challenging. This game style is very rare outside of stuff at the end of the 80s/early 90s, though.

[emphatic]

https://www.youtube.com/watch?v=x5J0bsQIo9E

[system11]

Vanguard II immediately springs to mind, as does Ark Area.

[Mortificator]

If you want to count games that allow you to stop moving, there's Sinistar and Raid on Bungeling Bay. I guess Desert Strike and its sequels are a bit like this too.

[gameoverDude]

I'll second Last Mission (Data East, see emphatic's youtube link above for some video) reminds me of TFII's sandbox levels.

Then there's ZugyA (X68000/Win). BTW the PC version "ZugyA DX" can be downloaded here at MIJET (where there's also an X68000 version translation patch).

[STK]

And I'll second Vanguard II. Even if the game is not as much fun as any of the Time Pilot games imo, I regret selling it.

[The Eidolon]

Have you tried Luftrausers? It's a modern game, but it has a little bit of a Time Pilot-like feel to me.
I enjoy playing it for survival more than score, but the combo system punishes you pretty heavily if
you don't string together enemy kills to keep your multiplier going.