I have heard that in the Midwest region of the United States (Nebraska, etc.), people do not have an accent when speaking compared to people from the south or either coast. Is this true? Why? Please add sources to back up what you say.
As a native speaker of Midwestern American English, I don't hear my accent as an "accent", naturally, but I know it's there. Any English speaker will recognize that I'm American as soon as I open my mouth and start talking English (I occasionally do better in other languages), and they'll probably recognize my accent as "Midwestern", if they've ever heard of it.
So it's not true that Midwesterners don't have accents; we do. As Schrödinger's Cat points out, everyone has an accent.
Possibly -- and here's the germ of truth in this myth -- it may be the fact that Midwestern English is the standard dialect for national broadcasting in the United States that people are referring to. Just as RP is standard on the BBC (with special exceptions for Northern dialects), Midwestern is standard in the US (with exceptions, mostly for Southern dialects).
Don't believe everything you hear about English. In fact, generally it's a good idea not to believe anything you hear about English; there's an awful lot of nonsense around.
Moreso than most any other country of the similar extent (maybe excepting Australia), the great majority of people in the US speak with the same accent. Only a trained language specialist (a student of accents like an actor or voice coach, not necessarily a linguist) would be able to take a random person and tell if they were different from the norm, much less say which variety the accent is from.
That is not to say that there are recognizable regional and cultural accents: multiple different but related varieties of Southern, the New York/New Jersey accents, the Boston/New England accents, the Northern cities accents, AAVE. But those are for the most part not that common or strong.
As far as the differences go, someone who speaks 'Midwestern' and someone who speaks 'General American' English are hardly distinguishable informally, but might be by taking a very specific and not terribly common set of contrasting pairs.
The only thing I have as an easy reference for this is the questionable wikipedia articles which really only give the distinctions rather than any perspective on prevalence: a section on regional differences, and a full article on regional accents. In the latter article there are two paragraphs describing General American English separately from Midwestern/Midland. There may be technical distinctions (cot-caught merger) but I find the distinction very subtle. They draw a distinction between North and South Midland; from my experience of both, their description sounds more like they are really describing the difference between General AmE and a variety of Southern AmE.
In sum, I find that the Midwestern accent, if one can really distinguish it, is very very close to General AmE, moreso than any other named variety. So I'd say that if anything could be called the Midwestern accent, though not identical, it is mostly indistinguishable from GenAmE for most people.
That said, a particularly notable (but arguable) example of the -North- Midland accent to the extreme is Sarah Palin (though from Alaska, she really sounds like she's from rural Illinois/Iowa/Wisconsin/Minnesota/Dakotas).