While saving an object containing the new Java 8 java.time.LocalDateTime, the following error is thrown :
org.springframework.core.convert.ConverterNotFoundException: 
    No converter found capable of converting 
               from type [java.time.LocalDateTime] to type [java.util.Date]
Tested
- Spring 4.3.2.RELEASE
- Spring Data MongoDB 1.9.2.RELEASE
Is Spring-data supporting the new Java 8 Date APIs (JSR-310)?
1. Spring Data + JSR-310
Yes, Spring-data supports the JSR-310 spec, with a custom convertor – Jsr310Converters, review the following code snippet :
CustomConversions.java
package org.springframework.data.mongodb.core.convert;
public class CustomConversions {
    /**
     * Creates a new {@link CustomConversions} instance registering the given converters.
     * 
     * @param converters
     */
    public CustomConversions(List<?> converters) {
        //...
        List<Object> toRegister = new ArrayList<Object>();
        // Add user provided converters to make sure they can override the defaults
        toRegister.addAll(converters);
        toRegister.add(CustomToStringConverter.INSTANCE);
        toRegister.addAll(MongoConverters.getConvertersToRegister());
        toRegister.addAll(JodaTimeConverters.getConvertersToRegister());
        toRegister.addAll(GeoConverters.getConvertersToRegister());
        toRegister.addAll(Jsr310Converters.getConvertersToRegister());
        toRegister.addAll(ThreeTenBackPortConverters.getConvertersToRegister());
        for (Object c : toRegister) {
            registerConversion(c);
        }
        //...
    }
2. Solution
The above Jsr310Converters will be enabled if you declared a Spring managed bean for MappingMongoConverter, and pass as an argument for MongoTemplate, review the following MongoConfig example :
MongoConfig.java
//...
import org.springframework.data.mongodb.core.convert.MappingMongoConverter;
@Configuration
@ComponentScan(basePackages = {"com.mkyong.db"})
public class MongoConfig {
    //...
    @Autowired
    MongoDbFactory mongoDbFactory;
    @Bean
    public MongoTemplate mongoTemplate() throws Exception {
        MongoTemplate mongoTemplate = new MongoTemplate(mongoDbFactory, getDefaultMongoConverter());
        return mongoTemplate;
    }
    @Bean
    public MappingMongoConverter getDefaultMongoConverter() throws Exception {
        MappingMongoConverter converter = new MappingMongoConverter(
                new DefaultDbRefResolver(mongoDbFactory), new MongoMappingContext());
        return converter;
    }
    //...
}
The MappingMongoConverter extends AbstractMongoConverter, and the AbstractMongoConverter is an InitializingBean. If this declared as a Spring managed bean via @Bean, the afterPropertiesSet() will be fired, and registered all the default convertors, including the Jsr310Converters
3. FAQs
If the MappingMongoConverter is not managed by Spring (init with a new keyword like below), you must call the .afterPropertiesSet() manually.
MongoConfig.java
@Configuration
@ComponentScan(basePackages = {"com.mkyong.db"})
public class MongoConfig {
    @Autowired
    MongoDbFactory mongoDbFactory;
    @Bean
    public MongoTemplate mongoTemplate() throws Exception {
        MappingMongoConverter converter = new MappingMongoConverter(
                new DefaultDbRefResolver(mongoDbFactory), new MongoMappingContext());
        //CALL THIS MANULLY, so that all the default convertors will be registered! 
        converter.afterPropertiesSet();
        MongoTemplate mongoTemplate = new MongoTemplate(mongoDbFactory, converter);
        return mongoTemplate;
    }
    //...
References
- Github – Custom converters to spring-data-mongodb
- Spring IO – MappingMongoConverter JavaDoc
- Spring IO – CustomConversions JavaDoc