Never really thought about it much, to be honest - but I would have thought that atleast some remnant of an advanced civilization would have survive intact/visible, but then again it would entirely depend on when it existed and what has happened to the surface of Mars since then - unfortunately, for there not to be any sign on the surface today (which there isn't), this would imply that the surface has undergone large-scale changes, and as such, it may be pretty unlikely that much evidence would remain intact for us to find anyway.
I've always thought that if humankind wanted to leave a permanent beacon, it would have to be put on the moon, because the surface of the Earth is a volatile, dynamic place that doesn't stay the same for very long (not on a cosmological timescale anyway)... the beacon would also have to be a broadcast rather than a safe deposit box - i.e. it would have to attract attention rather than just sit there awaiting discovery. If we are talking about a civilization on Mars that was on a par with mankind, I'd find it rather odd that they hadn't done something about marking their legacy for once they had left - a civilization that might spring up on Titan in 2 billion years time would know we had been here on Earth, not least because some visible remnants may remain, (we may even still be on Earth), but also for the many other signs we will have left behind - satellites, space debris, nuclear waste we've dumped out into the solar system raining down on them! If the Martians did exist, they certainly didn't do a very impressive job of making sure they were remembered...
One hypothesis (my favourite) is that there were (are!) Martians - handsome buggers too - who made contact with a superior alien race (like we are trying to do ourselves), but they demanded some form of 'Milky Way Council Tax' and the Martians faced eviction if they didn't pay up... so they left the solar system completely, leaving no forwarding address, and now reside elsewhere - the cosmic equivalent of Rio, perhaps. It's unlikely, but it's possible...!! Ironically, the reality of our survival may not be a million light years from that (unlikely) idea... we know that the Sun has a finite lifetime, and if we have any pretensions of outlasting the Sun, we will need to find that other place... literally not a "Home In The Sun", but atleast somewhere we can get a decent fry-up on a Sunday (excuse me, Nearest-Starday) morning...
- not to mention the fine-toothed comb 
