A document, usually a little booklet, that indicates your nationality and your vitals (name, birthday, etc.), and can get you through the customs officers in ports. In addition to a plethora of official stamps, a well-travelled person's passport usually has a good collection of visas and stapled-on temporary visas.

Passports are cool because they are like a record of all your travels. I had an Australian one stamped full of red, inside out. They are also of high-quality construction, laminated cover, and each page has its own watermark to prevent counterfeiting. The photo is usually dorky, but that is of no importance, because the most important thing about an old passport is how many stamps it has. Then again, maybe it's just me, because I travel too much.

I think I have four working passports right now. I usually use my Canadian one, but around Asia I use my Australian one. To get in the US, I use my permanent residency card, because it skips a lot of hassle (American customs officers are famously xenophobic). I also have a Hong Kong/British one that works well in Europe. The Chinese one is used around China, but nowhere else. Once, in the US, I pulled this one out instead of my residency card, and they submitted me to a full luggage search. I hate it when that happens.

The more the merrier. Collect them all!