I know 9600, 19200, 38400, 57600, 115200 and 1.8432 Mbaud, but no others. Why are these values used, and is it simply doubling each time or is there something more complex going on (for example, 38400 quadrupled is not 115200 baud?) 

The reason I ask this question is I'm designing something which may have to interact with a variety of different baud rates. It will initialise in 9600, and then switch to a specific baud rate. But I can't support arbitrary rates because the dsPIC33F I am using does not support arbitrary rates as it is limited to a 16-bit BRG down counter. It's similar in this regard to many other processors.

It started a long long time ago with teletypes — I think 75 baud. Then it's been mostly doubling ever since, with a  few fractional (x1.5) multiples, for example 28,800, where there were constraints on phone-line modem tech that didn't quite allow it to double.

Standard crystal values came from these early baudrates, and their availability dictates future rates. E.g.,

\$\begin{align}{7.3728 \,\mathrm{MHz} \over 16} &= 460,800 \;\text{baud}\\\\{7.3728 \,\mathrm{MHz} \over 64} &= 115,200 \,\text{baud}.\end{align}\$

Most UARTS use a clock of \$2^n \times 16\$ of the baudrate,  more modern parts (e.g. NXP LPC) have fractional dividers to get a wider range by using non-binary multiples.

Other common standards are 31,250 (MIDI) and 250K (DMX), both likely chosen as nice multiples of 'round' clocks like 1MHz etc.
