Another good library is JLanguageTool http://www.languagetool.org/usage/
It has a pretty simple api and does both spelling and grammar checking/suggestions.
JLanguageTool langTool = new JLanguageTool(Language.AMERICAN_ENGLISH);
langTool.activateDefaultPatternRules();
List<RuleMatch> matches = langTool.check("Hitchhiker's Guide tot he Galaxy");
for (RuleMatch match : matches) {
System.out.println("Potential error at line " +
match.getEndLine() + ", column " +
match.getColumn() + ": " + match.getMessage());
System.out.println("Suggested correction: " +
match.getSuggestedReplacements());
}
You can also use it to host your own spelling and grammar web service.