I got my first L- lens ~3 months after I bought my first DSLR (Canon 20D). As many others I am sure, I bought my first DSLR with a cheapo stock lens. After playing with it for a while, I was so disappointed with the results, I went out and bought 17-40 f/4L. Never picked up that stock lens again. It is a terrific wide-angle zoom and IMO better value than 16-35 f/2.8 if you shoot landscapes.
My first L series lens was my 70-200 f/4 that I still use today! It started me off into the dreaded "L Series Disease" that has fueled my passion for photography and kept my bank account money poor!
24-70 purchased not long after I got the 5D several years ago. I tried a bunch of Leica R lenses I had with an adapter - but wanted a good auto focus general purpose lens. It's great but heavy - really have to want a 2.8 to choose it over the longer reaching lighter IS 24-105. I do think the IQ may be a touch nicer with the 24-70 - or at least different and is very nice and I still use it often. 🙂
24-105 f/4. It turned out to be a great option as I can shoot pretty much any scene with it. It has great mid range coverage. I still have it on my camera when I go out, and only change to my other lenses when needed. It's a great lens.
My first L was about a year after my 30D. It was the 200mm 2.8, then I got a 70-200mm f/4. Sold both to go to 70-200mm f/2.8 which I still use. Also have 17-40, 24-70 and 300 f/4. Would love a 300 f/2.8.