Never got the whole 'Dodonpachi is great' thing. Always found it to have incredibly mediocre gameplay and mostly bland (in my opinion) artwork. Boring.
Shadow of the Beast on the other hand, despite not being that much fun to play and at times showing some badly dated pixelling has always captivated me with it's sort of dark fantasy otherworldly atmosphere (which is also greatly helped by the sound effects and music) and was a big influence on me at school. I haven't had the same sorta feeling from any 3D title I've ever played. An associate of mine showed a screenshot from his 'Beast Reborn' remake project a while back and he's a decent pixeller too. Ain't heard from him in a while though and I can't find the pic on my PC. Oh yeah and it's actually an influence on one of my current projects too (which I ain't shown anyone yet cept for some basic engine stuff... and won't show until I've got the atmosphere and graphic style the way I want it)
The animated intro to Shadow of the Beast 2 is still one of the creepiest things I've seen in a game.