A fine example of British engineering, the penny-farthing bicycle was invented in 1871 by James Starley. It was so named because the small and large wheels look like small and large coins, the farthing and the penny.
Not only are they more difficult to control, it takes both practice and a concerted effort just to get on one of the things. The large wheel, atop which is the seat in the original version, is just shy of being shoulder-height. The handlebars are so short and so important in steering (whatever you do, don't lean to turn!) that inexperienced riders often avoid turning altogether. Mounting a classic penny-farthing is usually done by tilting it to the side and jumping up on top of it, bringing it upright in the process. The trick is to keep it from falling back down on the other side. Of course you can't just put your foot down if you want to stop; you have to get off it, which is basically falling over and catching yourself.
The cult classic BBC show The Prisoner used a penny-farthing bicycle as its logo, and also a symbol during the show. The Prisoner's bicycle is one of the more sensible models, with the seat thrown back over the smaller rear wheel. It is shown with some sort of a cloth covering, which I believe is some sort of rain cover.