以为 and 认为 — thought wrongly, and think

規則 以为 = thought — and it nearly always means YOU WERE WRONG: 我以为你不来了，原来你来了。
认为 = consider, hold the view — neutral, for a considered opinion: 我认为这个办法可行。
So 我以为 keeps company with 原来, 其实 and 结果.
觉得 is the lightest of the three, a mere impression: 我觉得有点儿冷。