It is said that there is a quote somewhere by Tolkien stating that Elves have 'leaf-shaped' ears. But really, who can be bothered to track down things like that? And besides, Tolkien kept changing his mind about things. Any conclusions we draw about the shape of Elven ears should be taken from in-universe sources, not the author's discussions about it.
Fortunately, there is a very simple way to determine the shape of elven ears: comparative linguistics. Observe:
The earliest Elven language - Primitive Quendian - had a stem LAS. Four known PQ words are known which derive from this stem: ' lansrondo/lasrondo' (listener, eavesdropper), 'lasû' (a pair of ears), 'lassekwelêne' (autumn, literally 'leaf-fading'), and 'lassê' (leaf or ear). This connection between ears and leaves tells us plainly that the two have the same shape.
But wait! There are about as many shapes of leaves as there are leaves, period. Are we to be left forever bemused as to whether elven ears were shaped more like, say, oak or maple leaves? We have to dig deeper.
In Quenya, we find that 'ear' has become 'lár', while 'leaf' has remained the same, as 'lassë'. The word 'lasselanta' also exists, meaning 'autumn' - confirmation, if we needed it, that the 'leaf' in question is deciduous. No needle-shaped ears here! More interestingly, there is a word 'lassemista', 'leaf-grey', used by Quickbeam as a name for a Rowan-tree (alongside Carnimírië 'red-jewelled' and Orofarnë 'mountain-dwelling'. This gives us our first suggestion of the shape of the 'leaf'/ear - that of a Rowan-tree.
Still in Quenya, 'Legolas' is translated as 'Laiqualassë', both meaning 'Greenleaf'. The leaves Legolas was named after can thus be assumed to also be relevant. However, we cannot assume they were the leaves of Mirkwood, since Legolas could well have been born in Doriath (beech in Neldoreth, oak in Nivrim, holly in Region).
In Sindarin, 'ear' has become 'lhewig', with the dual form becoming 'lhaw'. 'Leaf' has become 'lass', while 'foliage' appears as 'golas', with plurals 'gelais' and 'golassath'. 'Autumn' once again uses the term ('lasbelin'), and we can find confirmation that Mirkwood bears leaves of the same kind - 'Eryn Lasgalen' is its later name, 'The Wood of Green Leaves'. Of course, since we don't know what kind of tree Mirkwood consisted of, this hardly helps.
Still, there is a consistent picture emerging. The rowan tree is explicitly associated with the 'ear' leaves, and there is at least a hypothetical link to the similarly-shaped beech leaves. The image of elves with pointed ears appears to be at least broadly accurate, though the question of whether they are elongated (Rowan) or more rounded (beech) remains somewhat open.
One final etymological curiosity: the word 'shoreline' in both languages appears as 'falas'. There is no known connection - but nor do we know the origin of 'falas'. Since Tolkien was fond of the beech tree, and since we speculate that beech is one bearer of 'ear'-style leaves - is it possible that 'falas' is a linguist's joke, naming the beach after the leaves of the beech?