Amateur Radio has a long, rich tradition of building things. Nowadays, that's a bit less likely, even though modern electronics may actually make it easier to build stuff -- a PIC is an amazing device.
However, antennas are still the prime purview of the builder, as they have been since Marconi's day. And it is in that venue that most of my own building has taken place.
Like most other modern hams, I started with an HT, and extending its reach was my first goal. I built my HT Whip, and with the counterpoise, it worked quite well. Buoyed by that success, I went on to build my first J-Pole antenna, and things have taken off from there.
One of my favorite antennas that I built was a tape measure antenna for fox hunting; I got the plans from here. It works quite well, and it's good for backcountry and ARES work, too.
In the near future, I will begin experimenting with quads and the Moxon Loop antenna, also called a Moxon Rectangle.
I first came across the Moxon Loop via L. B. Cebik's website; he has an amazing amount of material on antennas, and I focused on this one and this one. Moreover, there's a really good website for Moxon Loops at The Moxon Antenna Project.
I think a Moxon Loop antenna, made out of tape measure elements, and mounted vertically could make a really nice field antenna for ARES work. Simple, easily portable (the elements can roll up and reside in a 35mm film case. Not that those are all that prevalent anymore...) and fairly rugged. It's a nice design from Les Moxon, G6XN.