When new postings appear on this forum there's no obvious way of predicting whether or not they will generate/provoke a lot of responses. In the case of this topic, a fair number of the responses seem to stem from whether or not the responders have experience of dealing with stairway-related accidents or not, or at least information about such accidents. Though I've dealt with relatively few such accidents I think that stairways, an unavoidable feature in many workplaces, have considerable potential for significant injury as regards HOW people use them. Therefore, I can't agree with Clairel's comment at #23 that environment is the most important factor, not the person on the stairs. Surely much of OS&H in its widest sense is concerned with the physical aspects of workplaces, buildings, machinery, etc., plus behavioural aspects, i.e. how people interact (wittingly or unwittingly) with the physical aspects. Take fork lift trucks for example. Good design and maintenance of such trucks is important, as is the design and layout of the workplaces and routes they use, and equally the training and behaviour of their operators.
There's also a need to keep this matter in perspective. Stairways are so common that some people understandably think that safe use of them is a mundane topic, especially when compared with workplaces like nuclear power stations or North Sea oil platforms where activities and situations with potentially massive risks understandably and rightly get the most attention and resources to minimise such risks. Even so, it is appropriate for employers to try and influence how people use stairways, even though it surely is far from reasonably practicable to use observers or CCTV to identify stairway mis-users and tackle them.
Ron Hunter at #8 makes a very valid point about stairways near external doorways becoming hazardous when their steps are made slippery by moisture being tracked in on footwear from outside during wet weather. Employers with such stairways ought to have dust/moisture trap mats/carpeting just inside the doorways so as to try and control the stair slip hazard by physical means as much as possible. However, such physical control can become ineffective in cases where the mats become saturated with moisture because lots of people use the stairways and/or the wet weather continues for a long time. Therefore, stairway users may well need to be told/reminded that stairways may become more slippery than usual during wet weather and thus merit extra care. For people like myself who tend to run up and down stairs, such extra care means not running at such times.
Also, HSE might have an angle on stairway safety. While visiting a HSE office a few years ago I was intrigued to see an A4 size poster on a stairway I was using and took a photo, a somewhat mediocre one, of it, partly because I was still getting acquainted with a digital camera (one of my best tools for OS&H). The poster comprised a very simple cartoon with 4 figures running up/down 4 stairways interlinked in the style of the famous artist M C Escher, with a fifth figure shown plunging upside down from one of the stairways. Underneath was the advice "For your safety, please hold onto handrail". Perhaps the poster was devised locally because its heading was "Health and Safety Notice" which I thought was notably uninspiring. No doubt some forum users could think of alternative and inspiring headings.
Finally for now, here's a suggestion as a development of this topic: Why don't those of us with school connections (professionally or as parents of school age kids) suggest to schools, especially primary schools, that they hold competitions for pupils to devise a poster about stair safety? The posters could include aspects which can make stairs unsafe and also how ways of tackling the hazards. It seems that some children are more perceptive about such matters than adults might expect. Also, the posters would provide an opportunity for teachers to conduct interactive discussions with their classes about stair safety. If such competitions resulted in a reasonable proportion of today's kids having some grasp of stairway safety, then perhaps in the long term there might be less need for employers to consider trying to influence employees and others about such a matter!