What is the typical form for a finished Arduino project?
I'm in the same boat as you (SW engineer by trade who likes to tinker with electronics, and is a "maker" at heart.)

I think the answer to your question is "it depends." For a one-off, a breadboard might be fine.

For half-a-dozen, you might want to get project cases and perf-boards, and solder up your design. (For the Mega, there is a very nice prototyping "shield" that brings all the pins from the Mega up on headers and has quite a bit of working room for soldering up circuits.) If you want to make more than a handful, though, you'd probably want to create a custom PC board. You can either create a design in a CAD program and send it off to be small-batch manufactured, or you can buy the equipment to do it yourself. If you make hundreds of units, you should think about ditching the Arduinos and designing a completely custom board using the AVR-family microcontroller and only the components you need.

(I'm still at the breadboard/hand soldered perf-board stage myself, and haven't created any custom PC boards yet, just read about it.)