I've read that conflict over arable land was one of the main reasons that Greek city-states were often at war, but I was wondering if that was true, and if there were other common reasons?
The notion that the Greeks mainly fought over little strips of farmland is ingrained in older scholarship, tied up with the idea that Greek states were small and had small ambitions, with arable land being the main form of wealth known to them. From the middle of the Archaic period onward, mainland Greece was divided into hundreds of little states, most of which were separated by natural barriers such as mountain ranges or the sea. Each community occupied its own little valley, plain, or island. The few places where a border between states ran across accessible and fertile land, conflict was inevitably going to break out over where exactly that border should be drawn.
Indeed, we know a couple of good examples of exactly this kind of conflict. The so-called Lelantine War, mostly lost in the mists of time, was fought over control of the Lelantine plain on Euboea. For much of the 6th and 5th centuries BC, Sparta and Argos periodically fought over a bit of Peloponnesian farmland called Kynouria. Lokris and Phokis were often at war over grazing rights on the slopes of Mount Parnassos; for much of the Classical period, Athens and Boiotia fought over the borderland around Oropos. Herodotos (5.94) actually characterises Greek warfare in this way:
You [Spartans] should suspend your war, then, for worthless strips of land - for that fight with with the Messenians, who are matched in strength with you, and the Arkadians and Argives, men who have nothing in the way of gold or silver.
At first sight it seems hard to argue with this. Yet the Greeks fought many wars where possession of land doesn't seem to have been a factor at all. The most famous Greek war of all - the one against Troy - was fought over nothing but Helen and the honour of Menelaos. While this conflict is of course mythical, the motivation was very real to the Greeks. Communities and states felt slights to their honour very keenly, and much as we might like to think that such things can't have been the real causes of wars, the Greeks often presented them as such. The Spartans claimed that their war with the Messenians in the 8th century BC began over the rape of some Spartan girls; the Athenians argued the same to justify their conquest of Lemnos around 500 BC. One of the triggers of the Peloponnesian War was the Athenian support of Kerkyra in its conflict with its mother-city Corinth, which started because the Corinthians were insulted by the lack of honour they received from the Kerkyraians in their cult sacrifices.
A lot of this was to do with the critical importance of status in the greater community of Greek city-states. The ability to commit violence to further one's interests was an important pillar of such status, and the failure to avenge a slight was regarded as a sign of weakness. Within this system of values, far from using honour as an excuse for aggression, states were in fact more or less compelled to go to war over perceived insults to their honour and reputation. Many of the wars we know about were clearly presented as a matter of defence of a state's reputation or of enhancement of its status among the city-states. Standing up for one's friends and allies also falls under this category.
Indeed, when we look more closely at some of the conflicts that were ostensibly about farmland, we find that a lot of them actually seem to have been about status as well. Two communities on Samos fought a bitter war over a stretch of land that was literally called The Brambles - hardly the sort of arable farmland that would supposedly be indispensable to the Greeks. I mentioned the conflict between Sparta and Argos over Kynouria; when the Spartans finally conquered it, they gave it away to the Aiginetans who had been driven from their homes by the Athenians. They didn't need the land; they just wanted to be able to claim it was theirs, to dispose of as they saw fit (including for the benefit of their friends and allies). This was how they could improve their standing in the eyes of others.
Sheer desire for spoils of war was inevitably a factor as well, but it may have been of subordinate importance, simply because there wasn't much loot to be had. States that became the target of invasion tended to remove their livestock and possessions to a safe place, so that there was little to pillage in the countryside. Only if a settlement was captured could there be significant profit, mainly from sacking temples and selling the population into slavery. This explains the Herodotos quote above; profits in wars between Greek states were low. The speaker in that passage is trying to persuade the Spartans to attack Persia instead.
During the Classical period, we see a particular extension to the obsession with honour and status, which is that of hegemony. As single states (Sparta, Corinth, Athens) came to dominate large swathes of the Greek world, conflicts began to erupt over their relative standing and their spheres of influence, which were essentially upscaled versions of earlier conflicts to protect allies and preserve status. The Peloponnesian War is the prime example. Thucydides offers a lengthy discussion of the war's various causes, most of which have to do with slights to the honour of Corinth, Aigina and Megara; however, he himself believed that the "truest cause" of the war was "the growth of Athenian power, and the fear this inspired among the Spartans" (Thuc. 1.23.6). There is nothing here about farmland or spoils; no Spartan possession was even threatened. It sufficed that Sparta's allies were threatened, combined with a general sense that a single state couldn't be allowed to grow too powerful.
Finally, throughout their history, the Greeks were sometimes drawn into armed conflict because of perceived sacrilege. Offences against the gods angered all alike, and a few wars were undertaken to punish the offenders; those revolving around violations of Apollo's sanctuary at Delphi became known, appropriately, as the Sacred Wars. The most important of these was the Third Sacred War (356-346 BC), which began when the Phokians seized the temple and used the stockpile of dedications to fund a large mercenary army. This war dragged on for a decade, exhausted Phokis and Boiotia, and drew Philip II of Macedon into the affairs of mainland Greece.
If you'd like to know more about this subject, check out the discussion of both immediate and structural causes of wars in H. van Wees, Greek Warfare: Myths and Realities (2004) 19-43. For the specific role played by honour and revenge, see J.E. Lendon, 'Homeric vengeance and the outbreak of Greek wars', in H. van Wees (ed.), War and Violence in Ancient Greece (2000), 1-30.
How ancient are we looking at?
I've just done a module on the Peloponnesian War, if that's what you're interested in.