Hi Tuffers, Indeed, finding life from a different tree would be phenomenal. As it stands, all life that we know of and have investigated thoroughly originates from a single tree. Everything uses the same set of codons (with minor modifications), hence everything is built using the same "language", and can be said to be derived from the same pool of ancestors.
There are a number of possible alternative biochemistries that may have existed on the early earth, including alternative genetic materials (see the PNA- peptide nucleic acid- world, or TNA- threose nucleic acid- world), alternatives to the A, U/T, G, and C nucleobases, and alternatives to phosphates (arsenate- see Wolfe-Simon et al., International Journal of Astrobiology, 2009). However, our current biochemistry seems to be the most robust, hence evolutionary pressure would have selected us.
That's not to say that other biochemistries don't exist out there. Some "shadow life", like NosyNed highlights, would be hard to detect. Those forms of shadow life may use alternative handedness to their biomolecules, may use a different set of codons, or may even go more weird than that. Unfortunately, most of biological equipment is practical in nature, and hence tailored to understanding "typical" biochemistry, so searches for alternative life are quite limited.
As Mr Jack says, these three domains are still part of one tree of life. The biochemical similarities (RNA sequences, codon languange) between these domains are such that there's very little chance that these arose separately.
One idea I heard last year is that the three domains arose from a pool of common ancestors (see Just a moment... - note that this is not the best reference, but the conference where I heard this doesn't publish abstracts. The second author was the one who stated this idea). This idea varies somewhat from the fusion hypothesis in that eukaryotes arose about the same time as archea and bacteria, and suggests that mitochondria were absorbed shortly thereafter. Regardless, all three domains have one ancestral lineage.
Eric Smith gave the presentation on the pool idea, and I've had a hard time finding a paper which actually cites it, unfortunately. The small bit on the codons was as related as I can find.
I'll see if I can find something better- the presentation was in early 2008 so the idea may be in press or may never have left the ground. It was an intriguing hypothesis, but perhaps never made it past peer-review.