I'm surprised that no one has brought up the Lattice IceStick. It's an oversized USB stick with an ice40 FPGA on it and it's the cheapest option I've seen.
The cheapest options with much larger amount of logic are: Upduino v2.1 ($20) and the never dying EP2C5T144 board ($10).
The latter requires a USB blaster dongle to program things so the Upduino has the upper hand IMO, especially because it also has very lightweight open source tools.
The IceStick is also nice and a bit cheaper at ~$25 but it has a smaller 1k logic element Ice40 FPGA on it whereas the TinyFPGA-BX has a larger 8k logic element FPGA.
The latter requires a USB blaster dongle to program things so the Upduino has the upper hand IMO, especially because it also has very lightweight open source tools.