What are the candidates (and evidences) for ayaat which are claimed to be the last one revealed? I've heard so many opinions over the years, from Ma'idah:3 to Baqarah:281 to Surat Nasr and a few more.
There is no general conclusion on the matter. It depends, really, on who you ask.
If you go by Sahih al-Bukhari hadith:
Narrated Ibn `Abbas:
The last Verse (in the Qur'an) revealed to the Prophet was the Verse dealing with usury (i.e. Riba).
حَدَّثَنَا قَبِيصَةُ بْنُ عُقْبَةَ، حَدَّثَنَا سُفْيَانُ، عَنْ عَاصِمٍ، عَنِ الشَّعْبِيِّ، عَنِ ابْنِ عَبَّاسٍ ـ رضى الله عنهما ـ قَالَ آخِرُ آيَةٍ نَزَلَتْ عَلَى النَّبِيِّ صلى الله عليه وسلم آيَةُ الرِّبَا.
English reference: Vol. 6, Book 60, Hadith 67
Arabic reference: Book 65, Hadith 4586
Of course, this does not give the exact ayah.
Another common idea of the last verse revealed is the third ayah in surat Al-Ma'ida:
Prohibited to you are dead animals, blood, the flesh of swine, and that which has been dedicated to other than Allah, and [those animals] killed by strangling or by a violent blow or by a head-long fall or by the goring of horns, and those from which a wild animal has eaten, except what you [are able to] slaughter [before its death], and those which are sacrificed on stone altars, and [prohibited is] that you seek decision through divining arrows. That is grave disobedience. This day those who disbelieve have despaired of [defeating] your religion; so fear them not, but fear Me. This day I have perfected for you your religion and completed My favor upon you and have approved for you Islam as religion. But whoever is forced by severe hunger with no inclination to sin - then indeed, Allah is Forgiving and Merciful.
So as you can see, there is no general consensus on the idea of the final verse. You can see several claims here, and a somewhat logical conclusion, although it is not a scholarly conclusion.
The above answer seems to answer the question pretty well. I'll just add one tradition which is mentioned in Tafsir Tabari:
وقـيـل: هذه الآية أيضاً آخر آية نزلت من القرآن
It is said: This verse too, is the last revealed verse in the Quran.
The mentioned verse is:
وَاتَّقُوا يَوْمًا تُرْجَعُونَ فِيهِ إِلَى اللَّهِ ۖ ثُمَّ تُوَفَّىٰ كُلُّ نَفْسٍ مَّا كَسَبَتْ وَهُمْ لَا يُظْلَمُونَ
And fear a Day when you will be returned to Allah . Then every soul will be compensated for what it earned, and they will not be treated unjustly.