A big topic of interest these days is Ethernet cards for the Commodore 64. There are two main types; the ones that use the CS8900A chip (“RR-Net compatible”), and those that use the WIZnet W5100 chip. On the right (click to embiggen) are pictures of my machines with some of these cards: the Flyer (WIZnet chip), and a 1541 Ultimate V1 (with a CS8900A). The big problem with the CS8900A-based cards is that they require having a TCP/IP stack running on the Commodore, which is really quite a stretch, in terms of both speed and memory. The newer generation of cards is based on the WIZnet chip, which has an on-board network stack. The best of the batch so far seems to be the Flyer, which implements networking as I/O commands sent to device #7. (Unfortunately, it’s currently unavailable; I encourage you to contact Brandon and ask him to do another run of them.) I gave a presentation about this card at ECCC 2012, and discussed a reusable PROMAL module I wrote for the Flyer in my talk on that language at ECCC 2014.
Jonno Downes wrote Kipper BASIC and BASIC on Bails, which let you write networked programs for your Commodore 64 in BASIC. They only support the CS8900A-based (“RR-Net compatible”) network cards. I’ve put up a page about these projects with disk images, API docs, and a copy of the presentation I gave at ECCC 2010.
There are now wifi adapters available as well, based on the ESP8266 chip, although they generally seem to be nothing more than RS232-to-TCP/IP adapters rather than true network devices (there also seems to be little standardization of AT command extensions and even RS-232 implementations). Among them are Schema’s Commodore Wi-Fi Modem, CBMSTUFF’s WiModem, Melbourne Console Reproductions’ Telnet Wifi Adapter, and Alwyz’ Strikelink. You can also build your own Strikelink, or use Bo Zimmerman’s design. A card using Bo’s firmware is available here, along with some very complete documentation. More information on WiFi cards for the Commodore 64 can be found here.