I live in Finland, and we have possibly the lowest rate of "shots fired by police" in the world. In 2013 Finnish police shot only 6 times (https://yle.fi/uutiset/osasto/news/finnish_police_fired_guns_only_six_times_in_2013/7701005), and these 6 shots are from all the policemen COMBINED in a ~5 million population country. The reason for this is probably that if a policeman shoots their weapon, they have to go through an insane amount of paperwork conserning why did they shoot etc., and usually court too. So they actually only shoot when it's their last option. Also when a policeman fires his gun, it ALWAYS makes the top of national news immediately and remains as that for a couple of weeks at least.
They do carry tasers nowadays as you've mentioned, and they use them in situations when they can't get someone under control or arrested anyway else.
We also have VERY strict gun laws. No-one (except for policemen in duty) has the right to carry a firearm (or pretty much any weapon for that matter) in open in a public area. Also if you want purchase a firearm, you have to go through shooting training, and through a very specific examination by the police/government to get the license to purchase a gun. Basically if you've done pretty much any type of crime besides traffic violation in your past, you will NOT be able to purchase a firearm (legally).
This hasn't solved the problem of violence unfortunately. We've had several mass shootings (including school shootings) in the past 30 years. There are over half a million reported crimes each year (keep in mind there is only around 5 million people living here) in Finland according to the Ministry of the Interior (http://intermin.fi/en/police/crime-in-finland). And although firearms aren't easily acceptable legally, there is a LOT of firearms (especially from the WW2 era) still in circulation in "underground" markets. Also every summer many summer cabins are broken into and the main target for these robbers are usually hunting rifles and other firearms, because they hold such a high value in the black market. Also many people carry conceiled knives, peppersprays, tasers and other weapons in a possible situation where they need to protect themselves. And I guess we might be somewhat a notorious nation when it comes to barehanded violence (which is in many cases influenced by "Koskenkorva" ?).
So as we are in about all time low when it comes to police brutality and an all time high for gun control, our problem with crime and violence remains.