It depends how you define infinite.
In the 3+1 dimensional, single-reality Universe we see around us, no - the Universe is not infinite. There is a finite cosmological horizon, whose distance is determined by the speed of light and the time since the big bang.
This said, there are (at least) two other possiblities which may lead to an infinte Universe:
The first is the extra dimensions described by string theory. It seems likely that we are simply experiencing a 3-dimensional 'bubble' of spacetime, within a 10-dimensional larger Universe. Since we have no way (yet) of making observations of this larger Universe (ie probing into the extra dimensions) it is entirely possible that the extended Universe is infinite.
The second is the possiblity of parallel realities. Now, this may sound like something from a cheap sci-fi show, but quantum mechanics strongly implies that every possible quantum state IS realised at some place in the Universe, leading to an infilite number of 'weighted realities', which is constantly expanding in size. Richard Feynman was one of the first to pioneer this research.
Either way, we don't have a good enough understanding of the Universe yet to answer the question "is it infinite?". The best we can say is that the Universe we can observe is not infinite in geometric size.