Well, sometimes. I prefer David Cronenberg's 'The Fly' to the older one with Vincent Price, and given a push I'd probably pick the Coen's True Grit over the older John Wayne one. While Brian De Palma is in the mix, I'd bring up Scarface too, I realise that both films are wildly different and they may not fit the definition of a remake, but all the same, I feel De Palma ran with the idea better.
Also The Thing (with John Carpenter's being the remake, not the very recent one), that's a big one.
There's a lot of grey area on Michael Mann's Heat and his earlier film L.A. Takedown, which I guess could be ruled out somewhat seeing as they're made by the same guy and it's mostly just feedback-driven polish and better resources that put it in motion.
I think a few of those are down mostly to personal opinion, but there's a couple of undeniables lingering on the list too. Remakes are very, very rarely better than the original, but some can be surprising.