The simple answer is yes. Like all contact sports there is a high level of risk involved in the game and sadly there have been significant injuries resulting in paralysis and there have been some deaths
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Yes. In either code the game is a high contact sport and can and has had serious accidents with sadly some fatalities. However, the governing bodies do try to ensure that players take reasonable care of other players and has instructed referees to dismiss those found playing dangerously.
Broken fingers, thumbs, noses, collar bones along with cuts requiring stitches are a frequent occurrence. But as an ex-player I love the game - these things happen....
The answer is probably not 100% clear. In football the players wear helmets and other protective equipment, but as a result, they tend to hit far harder than they do in Rugby (either Rugby Union or Rugby League). Some evidence from U.S. High School teams suggests a lower injury rate for Rugby, though it could simply be that Rugby is on its best behavior since it is a fringe sport in the USA.
It is probably not as dangerous as you think, for there are rules regarding tackling.
The game compared to main ball sports is in the top 3 for injuries caused during play and training time