Watching live, without leaving the house
Three separate things get called "watching live": hearing the controllers, seeing the aircraft, and following where they're going. They come from different places.
Live ATC audio
LiveATC.net streams tower, ground, approach and centre frequencies from volunteer receivers around the world, and keeps an archive. It is the established source and it is free. Listening to air traffic control is legal in most countries but notably not in all of them — in the UK, for example, receiving aeronautical transmissions you aren't the intended recipient of sits awkwardly with the Wireless Telegraphy Act. Streaming sites are a separate question from holding a receiver yourself.
Airport cameras
A number of airports run official webcams, and several enthusiast channels run permanently staffed live streams with ATC audio mixed in — those are generally the best viewing, because someone is actually panning the camera. They come and go, so rather than list channels that will be dead in a year: search for the airport's ICAO code plus "live", and prefer a stream that names its frequency source.
Flight tracking
- Flightradar24 and FlightAware — the mainstream trackers, with free tiers that cover almost anything a spotter needs.
- ADS-B Exchange — unfiltered, community-run, and the usual choice when you want aircraft the commercial trackers suppress.
All three work because aircraft broadcast their own position over ADS-B in the clear. You can receive it yourself with a cheap SDR dongle and an antenna in a window, and feed it back to whichever network you prefer.
Which runway, and what's above you
- runwayinuse.com — works out the runway currently in use at an airport from ATIS, METAR wind, ADS-B traffic and NOTAMs, and shows the evidence behind the answer instead of guessing when the data is ambiguous. Useful before you set out; see spotting. Advisory only — it is not a navigation source.
- vfr3d.com — VFR sectional charts, airspace and terrain rendered in 3D. The quickest way to understand why traffic arrives over a particular ridge or why a class of airspace sits where it does, which is hard to see on a flat chart.