I see there being little-to-zero evidence that crop circles are extraterrestrial in origin. However, I also don't think the "Arecibo reply" was created by the same hoaxers who created the circular pattern ones. Much more likely it's a separate hoax perpetuated by bored astrophysicist graduate students.
Some remarks on your comments though:
BalthierTheGreat said:
There's sort of a problem here. DNA by the nature of the chemical bonds CAN'T have 3 strands. It would be unstable. The reason DNA is great for encoding our "program" is that the chemicals on one strand are directly complimentary to the other strand. When you reproduce the two halves of the DNA, you get two identical copies (in theory -- it still fucks up sometimes). Whith a third strand, there wouldn't be a way to copy the third strand, so that data would get lost.
That's not entirely true. I can imagine a system where a DNA strand of three parts splits in to those three parts, each gets copied twice, and they recombine (much in the same way our double helix does) in to three copies. Maybe then their cellular division would go three ways each time instead of two ways? :-)
Maybe they're so entirely different from us (mentally) that leaving crop circles seems like a reasonable way to proceed for them. For example, when we see an ant farm, there is no obvious leader, the colony is self-organising (a 'Queen' is in reality nothing more than a birthing machine, she's not the commander). Imagine ants that were as intelligent as us, living on another world. Who would we talk to? What might we do to communicate with such a civilisation? Might our efforts to communicate be interpreted in strange, wrong ways?
Maybe I'd send back pictures of something that "leaked" and just recently reached Earth. For example, the Gilse planet we found is 20 LY from earth, if the aliens are from Gilse, they could send back an image from TV from 1987.
It'd be from 1967. 20 years there, so in 1987 they'd be watching 1967 TV, which they could then send back to us, taking another 20 years, so arriving in 2007.
TV is a really hard thing to decode though. If you don't know the refresh rate (horizontally or vertically). Even if you could decode it, who knows what they'd see? Perhaps their eyes work on different frequencies. Perhaps they don't have eyes at all and use echo-location. Even if they do, perhaps they're giant floating bags of gas in a Jovian planetary atmosphere, and wouldn't recognize human beings as life-forms on a 2D projection of a 3D scene. Perhaps they don't use radio waves to communicate, perhaps they developed quantum communication or laser links first, as part of an utterly different technological history driven by different needs and different kinds of minds...
Also TV is very weak. It spreads out a lot, and by the time it's 20ly away, it may simply be too weak to detect. Much more likely that SETI will pick up a directed communications beam (of coherent radio waves) which has been sent at us on purpose or by accident. Even then, SETI don't monitor a huge part of the sky. From memory it's only a single-figure percentage, and a tiny portion of the electromagnetic spectrum.
I think it's extremely unlikely we'll ever pick up alien radio transmissions with current or near-future technology, except possibly by chance, without significant extra efforts. SETI is not a popular thing to fund versus fighting cancer or funding wars, though.
And even if we do receive something, who knows if we're able to understand or decipher it? The WOW Signal still remains a mystery, so perhaps we already have. If it is an alien transmission, we have no idea what it means.