Once in a while it's worth wondering what profound changes we're in for in the next decade if any. With that in mind, what's going to be the most common prosthetic in 2020 that none of us have today? Phones and smartphones are out of the running - we already all have those. Tablets are almost out of the running - or they would probably be the answer.
Let's exclude them - then what is it going to be? Or is the question wrong - like asking "what will be the most popular programming language in the home in 1990" in 1978? Will evolution be elsewhere? Won't technology be evolving in the prosthetic space at all?
My professional bet is on biohacks, but that might just be a little too science fictiony for a while to come. Other than that a swarm of chips around the phone seems likely to me. iPhone ready jackets and watches and glasses and pockets. 2020 might be too close for that. It might take another 5-10 years.
I like that you included that it must be common (not just "commercially available"). That makes it much more a question about standards competition, network economics, market share / monopoly power, politics, etc. than a question about technological development.
So we're talking MP3 playing car radios and catalytic exhaust systems, not flying or self-driving cars.
My guess: Memory aids with actually-usable search/navigation which will find the situation or forgotten memory and present the answer in video form (see note 1 below), as audio playback, or give a summary answer that has a high degree of context.
Example request: "The man in the purple shirt, where do I know him from?"
Answer: "You see him often in the supermarket. He buys unusual quantities of olive oil."
(If you asked a human friend the same question you'd get the answer "That's The Olive-Oil-Dude". Shorter, less explicit context, more personal, relies more on a shared understanding and insights about your usual level of memory recall)
Several different technologies would have to be improved and successfully combined to accomplish this, but the whole device can be built and marketed by one company (or a very small group of partner companies). I believe more in that scenario than in a "swarm of chips", because of the economical and political and technical complications of achieving a useful emergent result from combining many independent devices.
I think real politics (laws, regulations, bureaucracy, media outcry, etc.) will prevent any consumer technology product with a major bio- or medical component from being a commercial success in the short time span.
Note 1: Video would probably be reconstructed from a model, not an actual video recording played back. See for example this 2008 project http://research.microsoft.com/en-us/um/cambridge/projects/visionimagevideoediting/unwrap/