[apochromat]

So what's the furthest distance from me that anything in the universe can be?

[longshadow]

So what's the furthest distance from me that anything in the universe can be?

If the Inflationary Cosmology is correct, and thus the geometry of Space is Euclidean (or even if Inflation is wrong, but space is still Euclidean or Hyperbolic), there should be no limit on distance between two points in the Universe. If the Universe is closed, the maximum distance is finite.

Note: this is not the same as the maximum distance we can measure another object from us.

[apochromat]

In 1998, Pearlmutter announced a supernova that exploded 10 billion years ago and that was estimated to be 18 billion light years away. There must be a lot of dark energy acceleration at work to push it that far away, since light speed would limit things in the Universe to being 13 billion light years apart otherwise. The greater the acceleration, the larger the estimate should become, as far as I know.