Those interested in interstellar inquiry (which we really hope is all of you) should check out the METI discussion linked at the end of this post. The Benford brothers launch an interesting discussion on the costs and constraints of any communicating aliens, and while the idea of applying economic limitations to alien life is depressing it's well worth thinking about. There's also a discussion of the motivations for messages, and the sort of signal we should expect from each.
Thinking broadly, high-power transmitters might be built for wide variety of goals other than communication driven by curiosity. Here are a few examples:
Kilroy Was Here. These can be signatures verging on graffiti. Names chiseled into walls have survived from ancient times. More recently, we sent compact disks on interplanetary probes, often bearing people’s names and short messages that can endure for millennia.
High Church. These are designed for durability, to convey the culture’s highest achievements. The essential message is this was the best we did; remember it.
The Funeral Pyre: A civilization near the end of its life announces its existence.
Ozymandias: Here the motivation is sheer pride; the Beacon announces the existence of a high civilization,even though it may be extinct, and the Beacon tended by robots.
Help! Quite possibly societies that plan over time scales ~1000 years will foresee physical problems and wish to discover if others have surmounted them. An example is a civilization whose star is warming (as ours is), which may wish to move their planet outward with gravitational tugs. Many others are possible.
Leakage Radiation: These are unintentional, much like objects left accidentally in ancient sites and uncovered long after. They do carry messages, even if inadvertent: technological fingerprints. These can be not merely radio and television broadcasts radiating isotropically, which are weak, but deep space radar and beaming of energy over solar system distances. This includes “industrial” spaceship launchers, beam-driven sails, “planetary defense” radars scanning for killer asteroids, and cosmic power beaming driving interstellar starships with beams of lasers, millimeter or microwaves.
Believe and Join Us: Religion may be a galactic commonplace; after all, it is here. Seeking converts is common, too, and electromagnetic preaching fits a frequent meme.
Interstellar communication is no easy feat (assuming you haven't found any kind of space-time shortcut). People like to joke about how an aliens first look at us will be I Love Lucy or American Idol (in which case we'll be very lucky to avoid extermination), but physically it'd be easier for the alien to warp here and buy the DVDs. Television transmitters aren't exactly interstellar beacons. The most powerful transmission tower in the world only emits 2.5 Megawatts - assuming zero losses (and while you're at it wish for a unicorn), by the time the signal reaches the closest star it's spread out over 130 billion square kilometers, only twenty picowatts per square meter. Not even a trillionth of a lightbulb and, in case you haven't noticed, the only thing we can see that far away is stars.
We have to assume than any information we intercept is either intentionally beamed at us (or out at random) or based on technology we haven't imagined yet. We should really hope for the latter or it's going to be a long cold existence of extremely slow shouting at each things.