Originally Posted by
ChrisIII
It's basically a trial in which in-between the trial segments they "watch" three of the Doctor's adventures that are used as evidence against him. Although the entire serial is named "Trial of a Time Lord" the segments have been labeled differently in other sources.
1-4: "The Mysterious Planet": The Doctor and Peri find themselves on a planet that appears to be a post-apocalyptic Earth despite being in the wrong place.
5-8: "Mindwarp"- A sequel of sorts to "Vengeance on Varos". The Doctor is brainwashed into siding with Sil during an attempt to transport his leader into a new body.
9-12: "Terror of The Vervoids"-Set in the Doctor's future, the Doctor encounters a new species of genetically-engineered plant monsters onboard a spaceship.
13-14: "The Ultimate Foe"-With the help of the Master, the Doctor discovers the true reason behind his trial and the nature of the Valeyard.
There is also an earlier season long arc season 16, the Key To Time, which had the Doctor, K-9 and Romana, a Time Lady, seek out segments of a powerful object that are hidden across space and time. It has a three serial sequel, The Black Guardian Trilogy, in the middle of the Davison era.
There are also loose trilogies of stories here and there. E-Space during Tom's final season in which the Doctor, Romana, and K-9 get stuck in another universe, followed immediately by Keeper Of Traaken/Logopolis/Castrovalva deal with the re-emergence of the Master and the Fourth Doctor's regeneration, and the Black Guardian Trilogy during Peter's season which is a sequel to the Key To Time.. Also pretty much every Davros story in the original series is connected even going through multiple Doctors, and also includes a Dalek civil war.
The new series sort of uses arcs in a slightly similar way but it's mainly repeated phrases or visual clues culminating with a big reveal in the finales.
Season one-"Bad Wolf"
Season Two-"Torchwood"
Season Three-"Saxon"
Season 4-"She is returning/There's something on your back"
Specials-"HE will knock four times"
Season 5-"The Pandorica Opens"
Season 6-"Silence will fall"
Season 7-"Run, you clever boy, and remember".
Season 8-"Missy"
Season 9-Confession dial
Season 10-The vault
Season 11/12-Timeless Child
Season 13-Flux