I agree with Hoon that 겠 indicates your guess.
맛있겠다. I guess it tastes delicious.
When used with an action verb, you can take it as "shall" in English in my opinion.
You would not say 내가 가겠다(I shall go) with nothing following unless you're a general.
I'm thinking of a typical example... Suppose your friend is going to a grocery store and you asked your friend to buy something for you in a grocery store, but your friend would buy something else. Your friend went there again, but bought something else again. In this case, you would say 차라리 내가 가는 게 낫겠다 to mean "It SHALL be better for me to do it!"
Not really. I've found 모르겠다 interesting. My English-speaking friend has told me he was afraid to say it because it seemed to mean "I don't know"(blunt), but it's not blunt at all in Korean. This literally mean "I wouldn't know", it's a polite way of saying you don't know.