This coming Sunday (2014-07-06), London buses will stop accepting cash. So, be aware of that if you live outside London but you're planning to visit.
Some people are unhappy about this; I can understand the objections, but overall I think this is a good move. For instance, a few months ago I visited Sweden (on my way to/from the WSWC). Their buses don't accept cash, so they have SL Access cards instead: these are blue plastic cards, very similar to Oyster cards. Unfortunately, these weren't on sale at the ferry port, so I had a half-hour walk to the local town carrying all my luggage.
So, what happens if people don't have Oyster cards and they can't pay with cash? The simplest option is to use a "contactless" credit/debit card. These have a special symbol on them, which looks a bit like the symbol for a wireless network. I have 2 debit cards and 1 credit card from Lloyds, and they all have that symbol; I think that all the UK banks are now issuing them, and if your card doesn't have that symbol then you could ask your bank to replace it. I tested this last weekend, and it works exactly the same as an Oyster card: you just hold it against the card reader and wait for the machine to go "bleep".
The only snag is that bank cards don't have price capping (yet). If I use an Oyster card then it costs £1.45 for each bus journey, with a maximum of £4.40 per day, i.e. the 4th bus journey costs 5p and all subsequent bus journeys are free. If I use a bank card then it costs £1.45 for every bus journey, however many you take. (In my case, 5 journeys cost me £7.25.) I've heard some people suggest that TfL would like to abandon Oyster cards, on the basis that their job isn't to act as a bank, so they'd rather delegate that job to other people. However, I don't see that happening any time soon.
So, what happens if your Oyster card runs out of money (or you don't have one) and you don't have any bank cards with you? Or what if someone would prefer to make journeys without being tracked, e.g. if they have an abusive spouse? In that case, you could pay cash for a 1 day travelcard, i.e. you would get a little piece of cardboard rather than plastic.
But what happens if you don't have an Oyster card or a bank card or any cash? This actually happened to me a couple of months ago: my Oyster card ran low on credit, and I left my wallet at home by mistake so I couldn't top it up at a machine. That meant that I couldn't get on the bus, so I had to walk to the nearest station. (Normally I cycle to the station, so I just buy season tickets rather than travelcards, but this was the day after I'd been knocked off my bike and I had my left arm in a sling.)
If you have internet access (e.g. on a smartphone) then you could also top up your Oyster card online. However, there's a catch: you then have to swipe it at a station or tram stop to get the new balance; for some reason, you can't do that on a bus. Starting next Tuesday (2014-07-08), TfL will allow you to make 1 more journey with an Oyster card after your credit runs low. Also, if the bus driver considers that the passenger is "vulnerable" (e.g. a child travelling alone), they can issue an Unpaid Fare Notice; that means that the passenger writes down their name and address and then pays the money later.
So, what's the benefit of all this? As a passenger, Oyster journeys are cheaper than paying cash. I also think that the queue to board the bus moves a lot more quickly when people can just bleep their card and move on, rather than counting out coins. From the bus driver's point of view, it will make life easier for them if they don't get several people wanting to get change from £20 notes. Also, if they don't carry change, it may make them safer (i.e. nobody will try to mug them).
Anyway, we'll see what happens, but I think it will be ok.