There is dispute among Sunni scholars over the validity of Salatul Tasbih. The root of this dispute comes from differing views over the authenticity of this hadith:
The Messenger of Allah () said to al-Abbas ibn AbdulMuttalib: Abbas,
my uncle, shall I not give you, shall I not present to you, shall I
not donate to you, shall I not produce for you ten things? If you act
upon them, Allah will forgive you your sins, first and last, old and
new, involuntary and voluntary, small and great, secret and open.
These are the ten things: you should pray four rak'ahs, reciting in
each one Fatihat al-Kitab and a surah. When you finish the recitation
of the first rak'ah you should say fifteen times while standing:
"Glory be to Allah", "Praise be to Allah", "There is no god but
Allah", "Allah is most great". Then you should bow and say it ten
times while bowing. Then you should raise your head after bowing and
say it ten times. Then you should kneel down in prostration and say it
ten times while prostrating yourself. Then you should raise your head
after prostration and say it ten times. Then you should prostrate
yourself and say it ten times. Then you should raise your head after
prostrating and say it ten times in every rak'ah. You should do that
in four rak'ahs. If you can observe it once daily, do so; if not, then
once weekly; if not, then once a month; if not, then once a year; if
not, then once in your lifetime.
Sunan Abi Dawud
Some scholars such as Abu Dawud and Al-Albani have classified it as sahih (authentic), while others such as Ahmad ibn Hanbal and Ibn Taimiyah have classified it as da'eef (weak). Still, even the scholars that have considered Salatul Tasbih as valid have classified it as mustahab, so there is no sin attached if one does not perform it.
Source (Arabic):
http://www.islamweb.net/fatwa/index.php?page=showfatwa&Option=FatwaId&Id=2501
