I've always loved the woods. As a child I always wanted to own a bit of woodland - but then I think I was probably a bit odd.
I can't say I've ever felt any inexplicable frisson of fear in woodland, but I can see how it might easily happen. The timber below Gardom's Edge, and also Monk's Dale in the Peak District are two places that have always felt somewhat otherworldly. Also, the rather tautologically named Forest Wood around Lud's Church.
As Catseye has suggested, I suspect that our evolutionary history means that we're all only really a whisper away from flight mode in such environments.
On a slight aside - I once, many years ago, bivvied in the Black Wood of Rannoch. It wasn't the silence that got to me - quite the opposite, in fact. It sounded like an army were marching backwards and forwards through the trees. One of the noisiest night's I've ever experienced.
Some of the deepest, darkest woods I've come across were in Galicia and the Basque country of northern Spain. They really did look like brooding leviathans at night - pitch black and glowering over the villages, as if waiting to pour in when everyone is asleep. I think the atmosphere is partly emphasised by the fact that people don't really seem to use the countryside in the same way as we do in the UK (and it's generally less populated anyway) - so much of it seems utterly pathless and inaccessible, even when relatively close to human habitation.
And the Basques have their own bigfoot - Basajaun; utter nonsense of course, until you're up there on your own at night - and then definitely hiding behind a bloody big tree.