Others are recommending Gumshoe or Trail of Cthulhu. What it has going for it is that all the necessary clues are there and your players have the opportunity to keep digging until they get them all; this is in contrast to Call of Cthulhu, where you have a standard roll and either find the clue or not. I wouldnt be taken aback by Trail of Cthulhu (there is also Pelgrane's lesser known Fear Itself system) focus on HPL - thats easy enough to strip out.
But I think you can use almost any system for this kind of play provided one of the following -
- You have a skill system that supports investigative play (languages, lores, cultures, etc)
- You let the players play out non-combat encounters and use their own role playing skills to mine for information
I am running a very investigation focused OGL/3.5 game focused on a millennial plot. All characters have, if not "lore" type skills, also interpersonal skills (Bluff, etc) or perceptual skills that support it. As long as you have skills to roll, you can set the tone. But I think some who play using the engine will be predisposed towards typical themes so maybe its worth looking elsewhere.
The recently opened d6 system is very skills focused - you can usually "try" just about anything. Im currently working on a rules set based on it for a possible steampunk (non-fantasy) campaign. You can download the d6 Adventure rules from wegfansite.com for free.