"Misgiving" is a noun, and is always negative: it's a suspicion that something bad might be the case. It's often used in the plural. Example: "He said there would be no trouble, but I had misgivings." "Doubt" can be used in place of "misgiving", but it's more flexible. It can be a verb or noun, and (especially as a verb) can be used for any kind of uncertainty. For example: "I doubt we'll get into trouble." You can also use the phrase "in doubt" to mean "uncertain".

It is important to remember that "misgivings" often indicates or includes a sense of apprehension (worry). The Cambridge Advanced Learners Dictionary gives a good and simple definition: "a feeling of doubt or worry about a future event: Examples: Many teachers expressed serious misgivings about the new exams. My only misgiving is that we might not have enough time to do the job properly. The Oxford Dictionary adds that it can describe doubt or apprehension about the outcome or consequences of something. "Doubt" is just "A feeling of uncertainty or lack of conviction". No apprehension is included in its meaning. These are very accurate definitions. If you remember them, you will always be able to distinguish the two words and use them correctly.

Camilo- Doubt always have some uncertainty. "I don't know if it will rain, but I doubt it" .... I have doubt. Misgiving does not always have this, although it might. As Martin said, "misgiving" has a negative meaning about the future. If rain will be bad, I might have misgivings (bad feelings) about planning a walk because of my doubt (uncertainty).