1. Come and see me.
2. Come to see me.
3. Come see me.
[We use these patterns in imperative sentences. What about the following sentences? Can we use the following sentences as well?]
4. Let's go and take a look.
5. Let's go to take a look.
6. Let's go take a look.
[Are they all correct? Which one is commonly used?]
All three mean about the same thing. #3 is more casual.
I wouldn't use 5, but 4 and 6 are fine. #6 is probably the form most often used.