Basel is, in common with all Swiss cities, generally a safe place to be. If you do feel threatened, be sure you are somewhere you are seen such as a restaurant or bar or use a public phone: the emergency number is 117, and operators usually speak English.
Generally, the Swiss police are fairly discrete. However, traffic violations tend to treated seriously - jaywalking can be fined on the spot. As a result, drivers tend to be a considerate bunch and generally stop and crossings.
Football is the only real exception to this. FC Basel attracts a large following and football matches tend to be heavily policed by police in riot gear. Games are, however, generally safe just use your common sense and stay away from the hardcore hooligans who tend to occupy the cheap seats the can afford.
Trams are an important part of most Swiss towns and the public transport system. In my opinion, Baseler trams tend to be a bit quieter than most. There plenty of them about - especially around the Basel SBB, Barfüsserplatz, Marktplatz, Aeschenplatz, Messeplatz - so keep your eyes and ears open. If they ring their bells at you get out of their way. If you feel unsafe riding public transport late at night sit at the front near the driver - generally the drivers can be helpful if you're lost or in trouble.
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Mark Sukhija is a travel and wine blogger, photographer, tourism researcher, hat-touting, white-shirt-wearing, New Zealand fantatic and eclipse chaser. Aside from at least annual visits to New Zealand, Mark has seen eclipses in South Australia (2002), Libya (2006), China (2009) and Queensland (2012). After twelve years in Switzerland, Mark moved back to London in 2012. You can follow Mark on Twitter or Facebook