I used to have an A2000 with a 286 bridgeboard, on which I got TCP/IP networking running with an ISA ethernet card and the software to allow the Amiga side to use it, along with AmiTCP 4.3. It was a bit limited but allowed me to transfer ADF files over FTP, a lot faster than a serial link. I seem to recall that Aminet was available by FTP at the time too, which was useful.
More recently I’ve used my A1200 with a PCMCIA ethernet card, and with an Orinoco PCMCIA wifi card. I’ve still got all of this stuff (I can’t even imagine selling it), but I’ve not touched it in a long time. I even have a box full of Orinoco cards, as I thought they might have value to Amiga users so I could sell some of them. They’re Orinoco Silver cards though, so they only support 64-bit WEP encryption, although I suppose it’s not too much of a hassle to set up a separate wifi network just for the Amiga.
The most recent thing I tried was copying ADF files to an A500 Plus over serial using a Dell netbook and a USB-serial adapter, but I never got it to work right. I’ve got several laptops with hardware serial ports, so I really should use one of those.