I'd say that a dagger is a weapon of war in about the same way that a pistol is - primarily as a back-up weapon. And unlike a "knife" - which usually is a tool - a "dagger" is specifically made to be a weapon. Looking at medieval tomb effigies of knights in full martial attire, it is not uncommon to see them wearing a dagger along with a sword.
What was floating at the back of my head regarding Elves and daggers was indeed primarily references Legolas's "long knife". Whenever engaging in close combat, this seems to be the weapon he employs. And how Elves fought during earlier Ages notwithstanding, I can't recall exactly what other weapons they are seen using in LOTR.
That is exactly what I was implying. I was simply saying no warrior, Elf or otherwise, would use a dagger as a primary weapon. That kind of stuff works in modern D&D and anime, but less-so in a setting grounded in the realities of medieval warfare. Many characters are described as carrying daggers, but as was said by others in this thread, it's more of a tool and last resort weapon.
There are very few Elves whose arms are described specifically in Lord of the Rings, because other than Legolas, few Elves are featured doing anything martial in that story. Glorfindel drove the remaining Nazgul into the flooded Ford of Bruinen, but what weapon he was wielding -- if any -- is left undescribed as all that Frodo could see before falling unconscious was the Elf-lord's blazing fëa (though we can assume he wielded at least a sword as he did in the First Age). Haldir and his fellow Galadhrims' weapons are also not described during the escort of the Fellowship to Caras Galadhon, but considering Legolas's translation of their being able to "shoot (Sam) in the dark," we can probably assume they carried bows of the Galadhrim. Elladan and Elrohir rode with Aragorn to Minas Tirith, but again their arms were not detailed.
All of that said, much we know of Middle-earth has to be derived from and assumed consistent with Tolkien's other writings, letters, and compiled works from Christopher, and I see no reason not to assume that Elves in the Third Age would not arm themselves in the same way they did in ages past. That is to say we can likely assume Glorfindel wielded a sword as he did in Gondolin, the brothers swords and bows like the Rangers they so often rode with and as was standard for the Noldor, and the Galadhrim bows and likely swords or daggers (as was the custom of other Silvan Elves).