Iceland holds the European record for number of people with chlamydia STD, use a condom!
Iceland is considered one of the safest countries in the world. Just be sure to avoid the fights that break out amongst the most intoxicated partiers in bars and most often on the street on weekends. However most people are incredibly friendly and police are also friendly and very helpful.
Recently, however, petty thefts in Reykjavík have occasionally occurred. Rape occurs twice as often as in other Nordic countries, Still, even with these issues, Reykjavík is much safer than most other western cities, and certainly safer than the larger capitals of other countries.
Homeless people generally hang in the area around the Hlemmur bus station or on Austurvöllur park. They used to not bother anyone but have started doing so because people started giving them money; violence has occurred.
Lutheran churches are easily found throughout Reykjavík and most of them hold mass at 11am every Sunday. There is a Catholic cathedral in central Reykjavík by Túngata, usually called Landakot church but formally known as the Cathedral of Christ the King. A Catholic mass is held there every day in Icelandic, as well as a mass in English 6pm on Sundays and in Polish 1:15pm the second and fourth Sunday of each month. The Russian Orthodox congregation has a house at Sólvallagata 10, holding mass 6pm on Saturdays and 10:30am Sundays. There is no mosque in Reykjavík, but the Association of Muslims in Iceland holds Friday prayers at Ármúli 3, 3rd floor.
Even though Reykjavík doesn´t have a large population, traffic during rush hour 16:00-18:30 can be a nightmare. This is due to the exploding car population, along with a narrow street system. If you are planning on going somewhere by car or bus, try to do it after around 16:00-18:30 as this is when most of motorists arrive home from work. The same goes for the mornings 07:45-09:00.
Keep in mind that during the summer, the sun does not fully set, resulting in "dusk" between the hours of roughly Midnight and 3:00 AM. While a novelty at first, the lack of night can quickly disrupt your sleeping habits and result in general fatigue. If visiting in the summer, be sure to bring a sleeping mask, even if the window shades largely keep the light out.
If you can bear to be asked by almost every Icelander you meet "How do you like Iceland?" you're all set for the trip.
Reykjavík has one English language magazine, The Reykjavík Grapevine (http://www.grapevine.is), published bi-weekly in the summer and monthly in the winter. Although it started out as a publication mainly aimed at tourists with events listings etc. it has become respected in Iceland for at times very good research journalism and coverage of current events. Available for free at various locations around the city.
Some foreign newspapers are available at newsagents, but for same-day papers you can go to the Eymundsson bookstore at Austurstræti 18 and have them printed.
Reykjavík has good mobile phone coverage including 3G and various providers, the largest being Síminn (http://www.siminn.co.uk) and Vodafone (http://www.vodafone.is/en). Most foreign SIM cards should work without problems, but it may be best to check with your mobile phone provider at home before leaving. Payphones are almost nonexistant in Reykjavík.
Wi-fi is free at most cafés in Reykjavík and even at many bars. If there's a password required just ask the staff. Partly because of this, internet cafés have almost ceased to exist, but one such still in operation is GroundZero (http://www.gzero.is), Frakkastígur 8. Be aware that the clientèle is mostly gamers. 1 hour costs 600 kr.
Though Icelandic is the official language, English is spoken quite fluently by almost everyone you will meet and you should have no problems when it comes to communication.