List<String> nameList = ...    
String result = nameList.stream().collect(Collectors.joining("','", "'", "'"));

You can do it in two steps with StringUtils only,

List<String> s = new ArrayList<>();
s.add("one");
s.add("two");
s.add("three");

String step1 = StringUtils.join(s, "\", \"");// Join with ", "
String step2 = StringUtils.wrap(step1, "\"");// Wrap step1 with "

System.out.println(step2);

Output,

"one", "two", "three"

BUT

I need to pass them in a mongo DB query when using $in operator

For mongodb query you don't need to build it this way, specifically in case of $in you can query documents in following way,

BasicDBObject yourInQuery = new BasicDBObject();
yourInQuery.put("in_column", new BasicDBObject("$in", yourList));
DBCursor cursor = collection.find(yourInQuery);

Please read more about this in following link,

• Find or Query Data with Java Driver

Since Java 8:

String.join(",", slist);

From Apache Commons library:

import org.apache.commons.lang3.StringUtils

Use:

StringUtils.join(slist, ',');

Another similar question and answer here

Existing example and ones with replacing quotes can break if there are quotes in the strings themselves. You can use JSONArray to parse it and then convert to a list if needed

String x = "[\"role_A\",\"role_B\",\"role_C\"]";
JSONArray arr = new JSONArray(x);
List<String> list = new ArrayList<String>();
for (Object one : arr) {
    list.add((String)one);
}
System.out.println(list); //prints [role_A, role_B, role_C]
System.out.println(list.size()); //prints 3

json.jar can be found in the Maven repo

If I understand correctly, you're looking for something like:

String [] Country = New List<String>{'America','Australia','Canada','United Kingdom'}; 
system.debug('\'' + String.join(Country,'\',\'') + '\'');

Either write a simple method yourself, or use one of the various utilities out there.

Personally I use apache StringUtils (StringUtils.join)

edit: in Java 8, you don't need this at all anymore:

String joined = String.join(",", name);