I've played a number of Living Greyhawk games (i.e. the GM can't tailor encounters to you, and you may have a new party for each game) where we didn't have a rogue on the table. Sometimes it matters a lot, sometimes not at all, depending mostly on what sort of traps are in the module and whether you're required to make Search checks to find the treasure. Rogues have functions other than trapfinding, but trapfinding seems to be the only really irreplaceable one (as others have said, though, it's true that beguilers/scouts/etc can fill this role instead). Other PCs can do damage in melee (I don't know of any monsters especially vulnerable to sneak attack), and most skills can be covered sufficiently by the rest of the party. Having someone along who can open locks quickly and quietly is good, but rarely makes that much of a difference (Silence + adamantine weapon usually does the job, unless we're trying not to leave signs).
I think the time we were most severely punished for not having a rogue was when we triggered an Energy Drain x3 + Heightened Disintegrate x4 trap (EL 16ish, from memory, and it was protected against magical detection, so we didn't spot it with Arcane Sight). Fortunately most of the party had Death Ward armor and everyone made their Fort saves, but still, ow. That table was meant to be all-arcane (L15), but one player decided to bring his monk instead of his sorcerer, so we had a monk and five arcanists. The trap was right before a gauntlet of four EL 18-20 combats, and we were in hot pursuit of the bad guys, so no chance to rest - it was intended to be a difficult game.
Conversely, though, I played another game with some nasty traps with no rogue in the party - but those traps didn't have Nystul's Magic Aura on them. My sorcerer spotted the first Wail of the Banshee trap with Detect Magic, read off the Strong Necromancy aura, and volunteered to check it out because she had an auto-triggering Death Ward effect. She also asked the cleric for a Silence spell, guessing it might be Wail of the Banshee due to a divination we'd received earlier (about haunting wails guarding the door) - so that worked out well. The second trap was a spell turret, so we just bashed it to pieces with adamantine. When I ran that scenario for a friend's rogue, though, she trivialized both encounters by disarming everything.
So... YMMV. I'd always be pleased to see a rogue in the party, at any level, especially if I knew the GM used nasty custom traps. When you're meeting traps that have the same ELs as the combat encounters, just triggering them usually isn't a good option. I don't think any class is indispensable, though.
