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Although the shape of the universe is still a matter of debate in physical cosmology, based on the recent Wilkinson Microwave Anisotropy Probe (WMAP) measurements "We now know that the universe is flat with only a 0.4% margin of error", according to NASA scientists.
The model most theorists currently use is the so-called Friedmann–Lemaître–Robertson–Walker (FLRW) model. According to cosmologists, on this model the observational data best fit with the conclusion that the shape of the universe is infinite and flat.
I think the universe is a looped system. Once our telescopes can see far enough we will be able to see ourselves. Once this is understood it will throw a bunch of theories on the distance of objects in space into the recycle bin..