Travel safety advice is usually either alarmist or dismissive. The useful version is proportional: it spends most of its attention on the things that happen often and comparatively little on the things that make headlines.
The most likely problems
- Illness from food or water, or simply from exhaustion
- Road traffic, which is the leading cause of serious injury for travelers
- Opportunistic theft, particularly on crowded transport and at stations
- Losing documents or a phone
- Weather and terrain, in outdoor settings
Violent crime against visitors, which dominates the conversation, sits well below all of these in frequency in nearly every destination that people commonly visit.
Theft, handled sensibly
Split your money and cards between two places. Use a bag that closes properly and keep it in front of you on transport. Be alert at the exact moments thieves prefer: boarding a busy metro, standing at a viewpoint with your phone out, and the first ten minutes after arriving at a station with luggage.

Roads
If you rent a scooter in Southeast Asia, wear a helmet and check whether your insurance covers you, because most policies exclude it without an appropriate licence. As a pedestrian, remember that traffic direction and crossing conventions differ, and that in many cities a green signal does not mean turning vehicles will stop.
Health
Carry the medication you need, plus a copy of the prescription. Know the local emergency number. Check whether your destination has specific vaccination recommendations well ahead, since some require weeks. Drink more water than you think in hot climates, which prevents a surprising share of ruined afternoons.

Information sources
Government travel advisories are conservative but useful for a baseline, particularly on regional restrictions. Local news and your accommodation host will give you a more accurate picture of a specific neighbourhood than any general guidance can.
The overall approach: behave roughly as you would in a large city at home, adjust for local specifics, and do not let anxiety about improbable events push you into a smaller trip than you wanted.
Check the practical notes in each regional chapter before you go.