Uncanny seems to be the word I'm looking for to describe something, but I'm worried that it might have a negative connotation to it. Does it? What are some words that are very close to having the same meaning and don't have a negative connotation?
It usually has a negative connotation, but only a mild one. Close analogues would be words like:
A sentence like this does not have any particular negative connotation: "I was thinking about asking you to bring me a cup of tea not thirty seconds ago, and here you are with one -- it's uncanny!" In this context, the "uncanny" simply indicates amazement at the coincidence.
More commonly, it's used in sentences suggesting some kind of supernatural atmosphere or occurrence. For example, "We walked in and out, and took again and again a fresh look at the uncanny stones", suggesting a ring of stones with some magical or cryptic purpose.
It would be easier to judge whether uncanny is the right word for your purpose if we knew what you plan to say.
Although the word is used to express amazement and mild astonishment (as at someone's skill), it usually means that the reaction is at something that is disconcerting. NOAD:
uncanny |ˌənˈkanē| adjective ( -nier , -niest ) strange or mysterious, esp. in an unsettling way : an uncanny feeling that she was being watched.
It comes from a Scottish term referring to the occult, or something malicious.
An especially germane usage of this is found in "the uncanny valley" (found in discussion of computer-generated representations of human beings, such as in the film Polar Express):
The uncanny valley is a hypothesis in the field of robotics which holds that when robots and other facsimiles of humans look and act almost, but not perfectly, like actual humans, it causes a response of revulsion among human observers.1 The "valley" in question is a dip in a proposed graph of the positivity of human reaction as a function of a robot's lifelikeness.
EDIT to add graph of what the "uncanny valley" looks like (from the same Wikipedia article):