I heard One Step Closer on the radio when I was like 8 (back in 2000) and was hooked ever since. Later the album came out and I had my mom buy me that. It was my first album and I listened to it basically on repeat and from that point on they were my favorite band (until 2008 when I decided I liked Nine Inch Nails more - coincidentally, I only started listening to NIN after hearing Linkin Park's cover of Wish).
A few years after that, Meteora came out which was about when I discovered the LPU CD's as well.
When I was 12 I began remixing LP stuff and they are still the band I do the most remix work of.
When Rising Tied came out, it was the first hip-hop album I liked and it pushed me towards appreciating that genre much in the same way that MTM would eventually push me towards appreciating softer music a little while later. Minutes to Midnight was actually the first album leak I ever downloaded.
A Thousand Suns (and MTM to an extent) really changed the way I view LP's earlier albums. They really aren't anywhere near as interesting from a musical standpoint (whether that is a good or bad thing is up to the listener) which makes me not really like them as much anymore. I can still go back and listen to my favorites (OSC, APFMH, Faint, Figure.09, BTH) but it's kind of difficult to listen to those albums as a whole anymore.
In all, Linkin Park has really shaped the way I view music and what kind of music I like. Whether it's helping me discover my favorite band (NIN through the Wish cover), appreciating a new genre (hip-hop through The Rising Tied) or just expanding my musical tastes in general (Minutes to Midnight), Linkin Park has been a major influence on my music preference.
It's been a great 13 years of LP fandom and here's hoping they won't be gone anytime soon.