It is common knowledge that elves and dwarves don't like each other. But I'm curious if there were historical events which forged their views on each other in the lore of Forgotten Realms, or any other reasoning behind their relationship.
The answer by @That_Knight_Guy is complete indeed, nonetheless you may find more details in other source books.
Gold dwarves regard elves and half-elves with suspicion after generations spent battling their deep- dwelling cousins.
or about Shield Dwarves (pag 20)
Despite centuries of squabbling with elves and half-elves, shield dwarves have always managed to put aside their differences with the Tel-quessir in the face of outside threats.
It seems that this distrust of elves is due to the past (and present) conflicts between the majority of the Dwarf subraces and drows: the description of Urdunnir subrace (the closest ones to Nature and druidish culture) says (pag 22)
They are deeply suspicious of elves and half-elves thanks to centuries of dealing with their dark cousins.
On the other hand, I did not find so many details about the relation within Elves and Dwarves in the chapter devoted to Elves (pagg 26-47): just a short note about Wood Elves
Wood elves have a long history of cooperation with the shield dwarves, whose realm of Ammarindar stood alongside their own realm of Eaerlann for many centuries in the vale of the Delimbiyr River. By extension, they look favorably on most other dwarves, too.
Although this distrust, elves and dwarves formed some alliances for fighting orcs and goblins. For example, from Grand History of the Realms (pag 21)
–6400 DR The elves meet the dwarves of Sarphil on the battlefields of the Vast and forge a tenuous alliance since the elves save the dwarves from death at the orcs’ hands.
The history of the Severed Hand is about an alliance between the elves of the Hand of the Seldarine and the Dwarves of the Dorn's Deep: this alliance ended in a slaughter, orchestrated (again) by drows.
In conclusion, it seems to me that the main reason behind the turmoiled relation among Dwarves and Elves find its explanation in the drows' actions, past and present.
The races are not fond of each other, but respect each other
Dwarves tend to specialize over a long time and value ancient tradition while elves change their interest quickly. Dwarves don't take to humor very well, while elves are fond of it. Elves generally consider other races (Dwarves included) to be far less sophisticated than them. Each of these are a point of contention between the two races.
Both races consider each other a good ally when fighting orcs and goblins. Both races recognize that the other race has an aptitude for high quality smithing (though both races would argue their smiths produce higher quality goods)
While none of the core rulebooks go over any event in particular, they do shed some light on what is generally true for race relations and racial tendencies.
Player's handbook p.14 under the section Relations in the dwarf race
Dwarves fail to appreciate elves' subtlety and art, regarding elves as unpredictable, fickle, and flighty. Still, elves and dwarves have, through the ages, found common cause in battles against orcs, goblins, and gnolls; and elves have earned the dwarves' grudging respect.
Similarly from the Relations section of the elf race on page 15
Elves consider ... dwarves not at all fun.
Elves are not particular the way halflings and dwarves can be.
The text from these sections does not change between 3 and 3.5
While the 4th edition players handbook doesn't delve into race relations, it does have a relevant description of an elves personality.
Elves are a people of deeply felt but short-lived passions.
On page 19 of the player's handbook the dwarf race has a sidebar which contains a paragraph about elves
It's not wise to depend on the elves. No telling what an elf will do next; when the hammer meets the orc's head they're as apt to start singing as to pull out a sword.
... when orcs or goblins come streaming down out of the mountains, an elf's good to have at your back.
Page 23 has a similar sidebar in the elf race
Dwarves are dull, clumsy oafs. But what they lack in humor, sophistication, and manners, they make up in valor.