I am investigating on the best free mail library to use for Java web applications. It is something with more support and easy to use. If it\'s complex but would be justified by
Simple Java Mail which is a wrapper around Java Mail api:
https://github.com/bbottema/simple-java-mail (Maven Repository)
Does the Sun Javamail API not work for you?
http://java.sun.com/products/javamail/
"Best" is subjective, especially since you didn't specify any particular features you may be looking for.
With that said, here's a couple to get you started:
javaee.github curates a comprehensive list with many more:
Oracle has a curated list as well, although the lists are suspiciously similar:
JavaMail is the standard, but it is only a client, so you need to have a separate e-mail service to send mail. Asprin is a good implementation of a server.
EDIT: Asprin is a send only e-mail server. You can't use it as a full fledged POP or IMAP server. It just sends e-mail without any further third party (such as an ISP's mail service) dependencies (other than an internet connection). Unlike JavaMail, which requires you to have an SMTP server available to send e-mail for you (like from your ISP). If you need a full e-mail server, that can provide pop and imap e-mail, take a look at James.
Here is a list of java mail options, although most, like JavaMail, are clients, not stand alone solutions.