Some of these characters are mentioned in other groups; but just in case this question comes up, here are the characters who appear in the tournament for the Hand of the King (30 Sansa 2 and 31 Eddard 7):
Lord Yohn Royce and his sons Ser Andar and Ser Robar; Ser Robar hangs around the court and later gets sent out with a message for Robert about Clegane's raids (44 Eddard 11).
Lord Jason Mallister and his son Patrek.
Thoros of Myr, who wins the melee, thanks to his flaming sword.
Ser Balon Swann.
Lord Bryce Caron.
The twins Ser Horas and Ser Hobber Redwyne (who Sansa and Jeyne nickname "Horror" and "Slobber").
Six Freys, including Ser Jared, Ser Emmon, Ser Hosteen, Ser Danwell, Ser Perwyn, and Ser Theo; and Martyn Rivers, an illegitimate son of Walder Frey.
Jalabhar Xho, the exiled prince from the Summer Isles who hangs around court.
Lord Beric Dondarrion.
Lord Renly Baratheon, brother of the king.
We don't get a lot of Loras in this book; he's just a member of a powerful family (the Tyrells) who align themselves with young Renly Baratheon (70 Tyrion 9.49). But at the tournament, he shows us at least three important things:
(1) Cheating is a flexible concept. Loras is young (sixteen) and small compared to Ser Gregor Clegane, but he wins the joust because he messes with Clegane's horse. Of course, Gregor almost kills Loras for that, so there's a mixed message: you might win if you cheat, but you also might die when the other people decide not to follow the rules, too. (Also, cheating is awful and usually means more work than, well, not cheating.)
(2) That leads us to this not-so-revelatory revelation: Gregor Clegane is a dangerous guy. So we're not surprised when we hear that Clegane is raiding and killing people: that seems like the sort of hobby he would have. (Also, the fact that Sandor steps in to protect Loras tells us something about Sandor and Gregor's brotherly relationship.)
(3) Perhaps most importantly, Loras Tyrell helps emphasize how romantic Sansa is. When Sansa thinks about Loras, she sees him as "'the true hero […] a true hero, so slim and beautiful, with golden roses around his slender waist and his rich brown hair tumbling down into his eyes. And then Father had refused him!'" (45 Sansa 3.5). So, thanks to Loras, we see Sansa's romantic tendencies (how many times can she think the phrase "true hero"?), her shallowness (pretty = heroic), and the tension with her father.
About Ser Hugh, we only have this to say: ouch. Hugh was Jon Arryn's squire and maybe his poisoner as well. But we'll never know since Hugh dies in the tournament. Eddard suspects a bit of conspiracy about this; after all, Hugh was killed by Gregor Clegane, a Lannister soldier. But whether Ser Hugh's death is part of the conspiracy or not, his death is a sharp reminder (not as sharp as the lance that pierces his throat, but pretty sharp) that death is not a stranger in this book.