내게 is a contraction of 나에게, 나(I) + 에게(to), so it means "to me" in the simple case. In conversation, 나한테 is often used in place of 내게. - 그거 내게 줄래? = 그거 나한테 줄래?: Will you give that to me? - 내게 말해 봐 = 나한테 말해 봐: Why don't you tell me (about that). - 어머니가 나에게[나한테] 쓰신 편지: The letter my mother wrote me. 내게/나에게 has more uses than the above simple ones. To understand it fully, you need to know the usages of the particle(조사) "에게". ~에게 has three major uses according to the dictionary: 1. to (as in "something has an effect TO", or "belongs/pertains TO") - 그에게 무슨 일이 생겼나?: What happened to him? - 내게(는) 친구가 많다: I have many friends (There are many friends to/for me). 2. to (a direct destination/target of an action/effect) - 친구들에게 이 사실을 알렸다: I told my friends about this. - 돼지에게 먹이를 주었다: I gave forage to the pig. 3. from, with, by (a source of an action/effect) - 이 아이는 친구들에게 놀림을 받는다: This child is mocked by his friends. - 나는 개에게 물렸다: I was bitten by a dog. As you can see, ~에게 always involves a person or animal, and can be replaced by 한테 most of the time. #3 usage may be hard to understand, as it seems to indicate the opposite of #2 (to vs from). But both are common usages. In most cases the verb make the direction of effect clear, so it is not confusing.

내게 = 나에게 : To me, with me, For me... We commonly use '나에게'. Maybe '내게' is used in relics. 아빠가 나에게 연필을 사주었다. - Dad bought a pensil for me. 엄마가 나에게 공부하라고 했다. - She told me to study. 나에게 돌아와(Maybe in relic) - Come back to me. 그는 나에게 있어서 스승과 같은 존재이다. - To me, he is like a master.