From Discworld & Terry Pratchett Wiki
In a discussion about Dwarfs keeping up the old traditions, it is said that rich Dwarfs in non-Dwarfish professions, such as the clerical trade, will employ goblins to do nothing else other than hit small ceremonial anvils with small ceremonial hammers all day, purely to create the sort of atmosphere in which a Dwarf finds it easy to think.
They are also mentioned in Reaper Man in an excerpt from a Merchant's guild publication and as having delicatessen's in the Shades.
Secondly, Gnolls are explicitly described as a sort of stone-goblin. (Use of the word "goblin" supports the position that originally, Terry Pratchett intended them to be the Discworld analogue of Tolkien's Orcs, as they are vicious, sadistic, murderous, and attracted to filth). However, by the time of Jingo, all that appears to survive of this original concept is the attraction to filth and possibly a little residual cruelty.
In Unseen Academicals, a new race, possibly related to the goblins (but perhaps in much the same way that apes are related to monkeys) is introduced to the Discworld, although at the end we are told this is wrong.
This is refuted at the end of the book, where Lord Vetinari remarks that orcs must have been bred from men - only humanity has the inherent cruelty requisite for being subverted into orcishness; goblins are too small-time. TP really doesn't have that much respect for humankind...
Goblins are, in fact, a separate species from orcs and gnolls (although they may be related, in the same general way gargoyles and yetis are related to trolls) and are known to practice a religious life called unggue.
Ponder Stibbons once played the role of Third Goblin in a school play.
In Snuff, goblins, and their culture/religion are explored in greater depth. Their religion, unggue is based around the belief that everything that was once part of your body is always part of your body, and thus, it must be buried with you after death.
On the change of the nature of Gnolls through the books: there is a famous critical comment on Terry Pratchett's work, comparing him to Tolkien, but with the caveat that "in these Détènte-driven days, Pratchett has no horrors waiting to emerge from the East". (He doesn't have an East as such, in fact).
It could just be that an Orc-analogue simply wasn't needed - look at the way Elves have filled the niche for a non-human Other, which is inimical to mankind - and having introduced Gnolls in an earlier book, they simply got recycled to fill a different socio-ecological niche more suited to Discworld. Which as an argument holds really well together until you get to Unseen Academicals and have to rip it all up and start again, when a new race, which might originally have begun as Goblins (or men - see the article) but was seriously improved on by Igors working for the Dark Side, is introduced.