Wow, I've read so much hp fanfiction that it has all jumbled up into one huge mess. I can post links to the great fanfics that I can still remember though.
First of all I have to mention methods of rationality and chronicles of the king, even though those have been mentioned before. I've also read Mastermind hunting
http://www.fanfiction.net/s/2428341/1/M … nd-Hunting
Its a 600k word complete fanfic, harry is raised by dursleys, there is a lot of muggle technology its just really awesome.
To the person that was talking about Snape, you might like this one.
http://www.fanfiction.net/s/7724057/1/Family-Bonds
When, after that fateful Halloween night, the wrong Potter twin is hailed the Boy Who Lived, how will Harry's life turn out? With a power he knows not, an ancient prophecy and one Severus Snape practically raising him, interesting at least is a given.
There's another one lets see if I can find it...
http://www.fanfiction.net/s/4923158/1/3 … -Marauders
Harry & Dudley flee an abusive Vernon-to Severus Snape.Severus finds a new home for himself & the boys-with dragons and hunt the Horcruxes from there. The dragons-especially one become their allies. Tom R is VERY different.
Its also a really good fanfic, but it gets updated slowly.
And last is a harry potter and dragonriders of pern crossover, the first in the series is the queen who fell to earth:
http://www.fanfiction.net/s/7591040/1/T … l-to-Earth
Forced to compete and abandoned by his friends, he steps from the tent with only one goal in mind, suicide. Instead Harry awakens a power that spans time and space and starts a war between the worlds.
It, and its sequel are complete.
Sorry I didn't paste my own descriptions but I'm terrible at giving plot summaries. I'll just say that all of those are some of my favorite fanfics.
I'm probably gonna get banned for this, but...