Good to have, but a couple of caveats:
Some of the texts printed here are unreliable or even seriously wrong (#16 L-P, for instance). Much better presentation in David Campbell’s Greek Lyric vol.1 in the Loeb series. Is that not yet on line? If not it soon will be.
There have been important accessions too recent for inclusion either here or in Campbell. It’s an exciting time for Sappho.
Online as in the Loeb library? No idea, I try to avoid using the site - it’s so poorly designed. I don’t know what’s on the link I posted either, saw someone else post it so I just snatched it up. I can’t necessarily think of anything better online? I’ll ask around.
Thank you for this-Sappho, and all the Lyric poets are endlessly fascinating-I am especially interested in their context (what their world was like, seems much more interesting than any later period in Hellenic history) I devoutly wish someone would start up a Greek Lyric poets translation group-I would be willing to give up sleeping to take part in it.
It’s funny you post this, because I’ve been following James Stone’s “Playing Scrabble with Sappho” course with the Harvard Center for Hellenic Studies, and he mentioned that there’s very recently been a new, nearly complete Sappho poem released. I wonder if the author of the website you linked will include it.
Ten years ago the combination of a newly discovered papyrus with a previously known one gave us a poem complete except for the beginnings of its first four lines. It’s Sappho on growing old, known as the Tithonus poem (after the exemplum of the myth of Tithonus that it ends with—Tithonus was immune from dying but not from aging, oops).
http://community.middlebury.edu/~harris/sappho.new.html
Then just last year still more Sappho fragments turned up. They include the “Brothers” poem, about the safe arrival home of one of Sappho’s two brothers, an international trader. It’s complete except for a single stanza (possibly more) lost at the beginning.
http://www.the-tls.co.uk/tls/public/article1371516.ece
Exciting stuff, since there was only one complete Sappho poem known previously, and there seemed very little chance of getting more. Both poems show Sappho in a new light. Google “Sappho Tithonus poem” and “Sappho Brothers poem” for more sites.
CanadianGirl: choose your poet. I expect there’ll be interest. I’ll chip in but I’m not going to run it. 
The Brothers poem link needs authorization, sorry about that. So here’s the poem. It’s written in four-line stanzas, as you can see. Charaxos and Larichos were Sappho’s brothers, Charaxos an international wine merchant (Herodotus mentions him), Larichos evidently younger. She’s addressing someone, presumably a family member, mother at a guess but other guesses have been put forward.
… ( just one stanza missing?)
(1) ἀλλ’ ἄϊ θρύλησθα Χάραξον ἔλθην
νᾶϊ σὺν πλήαι. τὰ μέν οἴομαι Ζεῦς
οἶδε σύμπαντές τε θέοι· σὲ δ᾽οὐ χρῆ
ταῦτα νόησθαι,
(5) ἀλλὰ καὶ πέμπην ἔμε καὶ κέλεσθαι
πόλλα λίσσεσθαι βασίληαν Ἤραν
ἐξίκεσθαι τυίδε σάαν ἄγοντα
νᾶα Χάραξον
(9) κἄμμ’ ἐπεύρην ἀρτέμεας. τὰ δ’ ἄλλα
πάντα δαιμόνεσσιν ἐπιτρόπωμεν·
εὐδίαι γὰρ ἐκ μεγάλαν ἀήταν
αἶψα πέλονται.
(13) τῶν κε βόλληται βασίλευς Ὀλύμπω
δαίμον’ ἐκ πόνων ἐπάρωγον ἤδη
περτρόπην, κῆνοι μάκαρες πέλονται
καὶ πολύολβοι·
(20) κἄμμες, αἴ κε τὰν κεφάλαν ἀέρρη
Λάριχος καὶ δή ποτ᾽ ἄνηρ γένηται,
καὶ μάλ’ ἐκ πόλλαν βαρυθυμίαν κεν
αἶψα λύθειμεν.
(End of poem)
The next poem in the sequence is about the anguish of love, addressed to Aphrodite. This is more like the Sappho we know. But there’s very little of it left.