There is an interesting way to look at this question. By definition, two individuals are related only if they have a common ancestor. (If you mean something else by it, please correct me. For completeness, I include the trivial case in this: that is, I regard you as one of your own ancestors.) So your question can be inverted: it is really asking after how many generations everyone in the ancestral population is your ancestor?
As indicated in the comments, the answer will depend on the specifics of the population structure, including its size. But a first stab can be taken in this way: you had 2 ancestors one generation back, 4 two generations back, ..., $2^n$ (not necessarily distinct) $n$ generations back. So you certainly cannot be descended from everyone in the ancestral population if less than $\log_2 N$ generations have passed. ($N$ = population size, which for simplicity I assume to be stable.) In a freely mixing population under the very simplest assumptions, you will eventually decay exponentially towards complete coverage with a half-time of one generation.
This is complicated by the fact that some lineages die out completely. For instance, some of the individuals in the ancestral population didn't have any children. Some had children, but no grandchildren, etc. Obviously none of them were your ancestors, so you will never be related to them (except through previous common ancestors), no matter how much time passes. In fact, as time passes, more lineages tend to die out. So, if you look back very far, you'll find that the entire current population has only a very small numbers of ancestors in the distant past. This is called coalescence, and is what people are talking about when they speak of "mitochondrial Eve", for instance.
So, in summary, it's complicated. It takes only a fairly small number of generations ($O(\log_2 N)$) before you're potentially related to most of the ancestral population. But over longer times ($O(N)$ generations) your relationship to the ancestral population actually goes down.