For now it is only Cuban-Americans that can go (I REALLY would love to know where the Executive branch gets the Constitutional powers to limit where a citizen travels) but hopefully it will open to the rest of us "other Americans" soon. Damn I sooooo want to go. Not too mention that is a short general aviation flight from Florida.
You're not really prohibited from going, you just need a specific license to spend money there Academics go there all the time.
See Cuba on State's website.
As for flights, Cuba has seized GA aircraft "just because" as well as some personal boats.
Once relations normalize, however, sign me up, too!