There are countries without standing armies (i.e. Switzerland, I believe). They seem to be pretty secure.
There are very few nations in the world without a standing army and Switzerland is not one of them. Switzerland has an an active military component that serves to maintain training and readiness and nearly every citizen serves thier term as a part of it then goes into reserve status. These massive reserve forces can then be called into action very quickly and are backed up by one of the most extensive systems of fortifications and fallback bases ever devised including airfields built into the sides of mountains and civil defense complexes capable of holding the entire nation's population in the event of nuclear war. Switzerland hasn't been involved in a war since 1815 partly because the Swiss themselves made it suicidal for any other power to attempt invading thier territory.
Here's the Wikipedia entry, although I can cite a lot of other sources.
All able-bodied male Swiss citizens are conscripted to the armed forces. For women the service is voluntary. Since 1996, Swiss citizens can apply for civilian service instead. Entry to the civilian service is based on moral grounds and subject to a successful application.
A significant number of young men choose to avoid military service by visiting a doctor who attests to their incapacity to do military service on medical grounds, or try to fake it during recruitment through psychological and physical tests that are taken during recruitment. This can be on either physical or mental grounds. Those who are found unable to serve the military pay an additional 2% income tax, and must in any case serve in Civil Protection (Police, Fire Department etc.), though the duration of this is much shorter. As of January 2004, the income tax was raised to 3% by the Federal Council. Also, those who have conscience issues against war (for example, people who experienced violence at a young age, or have been in a warzone) can serve in Civil Service, where they do various kinds of social services, such as reconstructing cultural sites, helping the elderly and so on and so forth. However, a citizen may only request enrollment in Civil Service if they are psychologically and physically eligible for military service, but they have to put in one and a half times more time than they would as soldiers.
Conscription occurs at the age of 18 years. At the age of 20, about half the service is done during an initial training period of 21 or 18 weeks, depending on the service branch, with the exception of the Grenadiers, an elite infantry unit with a 25-week boot camp. Initial training (following regular boot camp) for members of the AAD, Switzerland's new SAS-type Special Forces unit, which is an all-volunteer professional unit with a rigorous selection process, is 18 months. Thereafter, men remain in the military until the age of 30 (or longer, if the military service is not yet completed), performing three weeks of training every year. However, the service period of non-commissioned officers and officers is significantly longer. Due to a new military reform enacted in 2005, it is no longer possible to postpone the initial training to finish university, although it is possible to postpone in order to finish highschool or equivalent internships (for example for an aspiring carpenter who might only finish training at 19 or 20). For this reason many people try to get out of military service, so they can attend university immediately after finishing highschool. It is possible to split the time in basic training (as recruit) and service (as soldier) which would allow one to start university immediately, the second half must be served at the earliest possible opportunity, usually Christmas break, a time which is usually used to study for exams. Hence, this practice is very hard on the student, and generally not recommended. The successive training weeks can also be postponed, but there is limited scope. In general, men interrupt their work during these weeks. During military service, the employee is paid a compensation of 80% of his regular salary by the state. Most employers, however, continue to pay the full salary during military service. In this case, the compensation is paid to the employer
The few nations without standing armies are either nations with protection agreements with larger, more powerful nations like Iceland (a NATO member) or Andorra(which relies upon protection agreements with Spain and France), completely isolated nations with no neighbors like Iceland and Barbados that still have treaties with larger nations(in Barbados's case the UK) or nations with something else that serves the same role like Costa Rica's National Guard.