If you've got no place to go, today is a textbook winter wonderland in London. If, like most people, you've got to travel in for work, well the going is still tough. It seems to have been pretty widely established that certain train companies are, let's say, playing coy with information, so your best bet is to get updates from Twitter.
The rail networks are, of course, most severely affected. Southern trains have NO SERVICES WHATSOEVER until 10am, and then only if you're lucky (follow on Twitter). Southeastern have some services, but reports don't look good (follow on Twitter). FirstCapitalConnect has reasonable, if crowded, services from north of London, but the route down to Brighton is completely blocked (follow on Twitter). Other operators appear to be doing relatively well, but let us know in the comments if you've had other experiences.
The Tube is mostly working, although 'severe delays' are affecting the Circle, Hammersmith & City, and Jubilee (to compound problems for the south-east).
The DLR is reportedly working fine. However, because it's about the only thing that is, some stations and trains are suffering overcrowding.
Buses? Other vehicles? You tell us.
Image by version3point1 in the Londonist Flickr pool.