This is an example which comes directly from the doc. When i just set "size=1" to get my drop down, the "test" button doesn't get involve.

 public class sampleCon {

 	String countries;
...	
        public String getCountries() {
  	 	return countries;
 	}

 	public void setCountries(String countries) {
 	 	this.countries = countries;
 	}
}

public PageReference test() { system.debug('countries===>' + countries); return null; } public List<SelectOption> getItems() { List<SelectOption> options = new List<SelectOption>(); options.add(new SelectOption('US','US')); options.add(new SelectOption('CANADA','Canada')); options.add(new SelectOption('MEXICO','Mexico')); return options; } public String[] getCountries() { return countries; } public void setCountries(String[] countries) { this.countries = countries; } }

<apex:page controller="sampleCon">
 	<apex:form>
 	 	<apex:selectCheckboxes value="{!countries}" size="1">
 	 	 	<apex:selectOptions value="{!items}"/>
 	 	</apex:selectCheckboxes><br/>
 	 	<apex:commandButton value="Test" action="{!test}" rerender="out" status="status"/>
 	</apex:form>
 	<apex:outputPanel id="out">
 	 	<apex:actionstatus id="status" startText="testing...">
 	 	 	<apex:facet name="stop">
 	 	 	 	<apex:outputPanel>
 	 	 	 	 	<p>You have selected:</p>
 	 	 	 	 	<apex:dataList value="{!countries}" var="c">{!c}</apex:dataList>
 	 	 	 	</apex:outputPanel>
 	 	 	</apex:facet>
 	 	</apex:actionstatus>
 	</apex:outputPanel>
</apex:page>	

Since multipick is now false,  So figure that I have to change the set and get to accept string and not string[];

Now i get this error:

SampleCon Compile Error: The method void setCountries(LIST<String>) is referenced by Visualforce Page (sampleCon) in salesforce.com