Technically it's possible to walk to and from any airport. The main question would be how much risk or effort you want to put into it. For example, you can walk to Heathrow terminals 1-3, but it'd be a suicide mission. Besides, it's just £1 or so with an Oyster card on the Piccadilly line from Hatton Cross. Terminal 4 would be much more walkable (yet still madness). You have then walked to the airport and can just get on the tube from there to reach other terminals.
Other airports I'd absolutely won't walk to are FDE (it's a 20 km or so uphill walk), OSL (a 50 km walk to downtown), JNB (have to go through a township to get downtown, which basically also is a ghetto), ARN (also a very, very long walk), AAR (30 km to town) and MFM (sure, it's walkable, but there are loads of free luxury hotel shuttles
).