I'll answer too... although I'm going to repeat many of the answers.

They're not in a specific order.
1) I think it's a great tribute to an unknown Spaniard. Unknown in his country, at least. And I think (at least) the heli world and Spain owes a lot to this man, who lived for his passion and his country, so this is my way of giving him some credit and make his ideas live.
2) It's different, uncommon and unknown. That's very good in some senses, but also gives some troubles. You're the only one in the field who flys them (often you're the first gironut they meet). People, in best cases have very little knowledge about them and ask things. That doesn't bother me, as I like to share my little knowledge with those who show true interest. Others, instead of being modest and saying they don't know nothing about them, cover their ignorance with imagination (it's quite fun to talk to them

). A few others will run away scared at the sight of the swirling menace and even point a cross at you and shout biblical jargon for even mentioning the name of the flying device. Of course, there is the "experts crowd" or "wise men council", don't know how you call them here, that will come over, look over like you need their aproval, and start talking bullsh** about your autogiro. They don't know nothing about them, but will give their definitive pro advice about random things like engine incidence, blade profile, history, flight theory and/or flying tips (my favorites

!!!!). Don't even think of crashing, as they will start again saying "I told you..." and repeat the pre-flight briefing again, giving their obviously correct explanation for the incident. I'm lucky, I fly alone and the two times I crashed the repairs were nearly aesthetic.
3) They're challenging! They aren't designed or flown like planes, even less helis. Construction can be quite similar to the first, though. The design is quite more difficutl than on planes, because you have fewer references, they're more critical (=it's more difficult to make a sound design in general) and I think you need a higher degree of understanding to know what you are going to do.
4) They have very appealing flight characteristics! On one ocasion, I was flying at sunset. The autogiro was barely visible in the sky, but it was time to land and I made it come down towards the field. Then, when it reached the height of trees, it disappeared in the dark. I couldn't see anything at all. I had my ECDC giro very well trimmed, so I gave him my trust (as if I had other options!) and let the hands of the stick. After a few seconds, I walked towards where I thought it landed and guess what: it was a perfect landing! The blades where still turning and the prop idling with a nice poping sound. Landings aside, being able to make ultra-slow fly-bys, vertical or backwards descents, etc. are very atractive to me. I even enjoy take offs! I always TO from the ground.
5) The sound of the blades. I just love it. I'm starting to think I'll have to make something to the tips of my blades so they whistle or scream louder.
6) James Bond flys one. Enough said.
And, of course,
7) Just because I want to do it!
PS1. Floridagyro, IMHO it seems like you need some negative incidence in that motor.
PS2. Imsofaman, the correct, full name of the inventor is "Juan de la Cierva y Codorniu" (name, surname of father and surname of mother), or just "Juan de la Cierva" if you prefer. But "Juan Cierva" is a bit "incomplete".