Is there any difference between 想, 觉得 and 以为?
以为 is mostly used for: 


wrongly thought/believed 


like: 我以为你死了！ I thought you were dead!

觉得 is closer to:


feel/think (of an opinion)


like: 你这样说，我觉得非常不靠谱 What you said is totally unreasonable.

想 is close to the English:


think


like: 我想这个案子肯定有猫腻。 There's something fishy about this case.

In Chinese the idea of English 'think' is hardly ever used - even in English it's mostly just a buffer or fluff; if anything 觉得 is the closest.