Any microcontrollers which can be directly programmed on a breadboard?
Most (all?) NXP LPC ARM and Cortex microcontollers have a built-in serial bootloader. You will have to provide the UART signals to these chips at 3v3 (NOT at RS232 levels).

The LPC1343 also has a built-in USB bootloader: it can present itself as a drive, you simply copy your firmware to it. Sounds simple, but a bit tedious in practice if you want to do this often. 

For most microcontrollers bootloader software is available (in most cases multiple versions). You (or someone else) must first download this software to the chip. In most (but not all) cases you will have to configure your application to work with the bootloader (not occupy the same addresses).

I once wrote a bootloader called ZPL (zero pin loader) that interfaced to its host only by its reset pin. It timed the interval between the resets, and decoded the bitstream from this timing. The reset signal was provided by a UART signal from the PC. IIRC this idea was not mine, I read (or at least thought I read) somewhere about a bootloader using only the reset pin. Once you know (or think that you know) that it is possible the reset is just work.