Possibly you'll have problems with characters like ASCII STOP and such non-printing characters, but if you use prepared statements and parameter binding, you won't have any trouble even with characters like '.
If you don't want to use parameter binding and prepared statements, you can replace all of your input ' with \' and you'll be fine.
SQL typically uses ' as its special character to tell when a string literal starts or stops. If your input has this character, it will stop treating the current line as a string and start treating it as commands. This is not a good thing, security wise. It also keeps you from inputting that character unless you "escape" it by placing a backslash in front of it, which tells SQL to ignore the ' and continue treating the following characters as a string until an unescaped ' is met. Of course, backslash literals are also escaped as double-backslashes.
Prepared statements typically look like this:
String sql = "INSERT INTO MYTABLE (NAME, EMP_NO, DATE_HIRED) VALUES (?, ?, ?)";
PreparedStatement ps = sqlite.prepareStatement(sql);
ps.setString(1, myString);
ps.setInt(2, myInt);
ps.setDate(3, myDate);
ps.executeUpdate();
Unfortunately, I don't know exactly what library you'd be using to access sqlite from Android, so I can't give you more details at this time.