While out in Europe for the past couple years, travelin' about, I used a hammock/tarp combo. For hitchhiking I found a tarp to be a lot more versatile, low profile, situational awareness is much better (no doors!), when it's raining you're free to move around a LOT more, and when it comes to the law police ( from my experience) seem to care less about a tarp and more about a tent. In europe that whole camping vs bivying thing can be pretty grey in their eyes.
The biggest downsides to a tarp are NEEDING a fence/tree/pole to keep it propped up, mostly. If it's pissing rain it's a definite. In high winds you better have a tarp staked down well... Going through a storm in a tarp is not so great. Tents have bugnets, can prop up just about anywhere (given space), and can be a few temperatures higher inside (or more if you do the candle thang).
For me, I just don't think I could tent it long-term. Too many reasons to go the tarp way.
I also have the US army bivy bag. Got it for about $24 from
http://www.hassayampasurplus.com/ (can't see them there anymore). Haven't used it yet, but during my time in the Canadian army, our bivvies were absolutely beautiful. I would say take a tarp or a poncho with you as well, as having a bivy as your only shelter would restrict you a lot and confine you to such a small place... If it rains for hours or days you aren't going to be so happy.
For my next big trip (around the world by hitchin') I will either take my bivy and a tarp/poncho, or keep my eyes out for a good hammock (mine is good, but it's not so great for pitching on the ground as tent as it lakes tent poles... which I could also look for). There is a thing in development, the "alpine hammock" (google it) which is basically a tent in hammock form. Looks like it could be pretty good.
