Sugoi (すごい)

すごい is a commonly used word to mean "great". It is used when people is surprised or excited about something. It can have positive or negative meanings, depending on the context. So it can be translated to "great", "excellent", "cool" in a positive context, and "terrible", "horrible" in a negative context.
Example:
すごい = That's great! / That's horrible!
すごいでしょう= Isn't it great?
すごい映画 = A great movie

すごい is also often used in front of an adjective to mean "very". When used in this way, its form is changed to すごく (change the い to く).
Example:
おいしかった = That was delicious
すごくおいしかった = That was very delicious
美しい女性 = a beautiful lady
すごく美しい女性 = a very beautiful lady

The slang version of すごい is すげえ. This should only be used in informal conversations. And since it is a slang, there is no need to follow grammar rules when used in front of an adjective.
Example:
すげえおいしかった = That was very delicious