Du'a ( Prayer before the salaam )

Are encouraged to pray before the salaam ?
Yes. Sunnah prayer - which - with the following prayer ;
اللهم إني أعوذ بك من عذاب جهنم , ومن عذاب القبر , ومن فتنة المحيا والممات , ومن شر فتنة المسيح الدجال" O Allah ! I seek refuge with You from the punishment of hell fire , from the torment of the grave , from the trial / test when life and death and from the evil of Dajjal defamation " .
In a hadith narrated by Abu Hurairah , the Prophet said : " When someone you finish the reading tasyahhud (ie tahiyyat ) end , then seek refuge with Allah from four : from the punishment of Hell , from the torment of the grave , from the trial of life and death and from the evil of the Antichrist " . (Reported by Imam Muslim )
In addition to the above prayer , prayer other Prophet ever read are;
اللهم اغفر لي ما قدمت وما أخرت , وما أسررت وما أعلنت , وما أسرفت , وما أنت أعلم به مني , أنت المقدم وأنت المؤخر , لا إله إلا أنت ." Oh God . Grant me forgiveness for whatever ( sins ) which I did earlier and the later, which I will hide and that I seem at least as well as whatever act or extreme vanity which I do thou any more to know about it from my own . You are mighty before God and the almighty end . There is no God but Thee alone " .( Narrated by Imam Muslim from Sayyidina ' Ali r.a. )

http://fiqh-am.blogspot.com/2008/06/solat-doa-sebelum-memberi-salam.html