I was at the park today and was wondering what the record for most valid FastPasses in one day is for one park. I've gotten 3 max, but I've never tried for more.
If you go on a slow day, you can get basically one every thirty minutes the park is open, and then add more to that with the unlinked machines if you really wanted to. Of course, you wouldn't actually need to use these Fastpasses, as there would be no line to do so ever.
On a slow day that I visited, I was able to pick up four Fastpasses on a 10:00 opening by 11:50. Since I quickly realized how lucky I was and that they weren't going to have long lines all day, my group just picked up one more after that to have one from each ride that we did.
We recently got 9 for the 18 rides (including multiple trips on the same ride), but that was for both parks combined.
Arriving a little after opening on a somewhat crowded day at Disneyland only, you can get at least one Fastpass for every attraction that offers one, but you'd have to go after less-desirable rides like Roger Rabbit and Big Thunder multiple times if you wanted to maximize the number of Fastpasses you collected. Of course those rides have periods where you don't even need a Fastpass so there isn't much point in getting them.
For a reasonable plan, I'd say you could get maybe 5 before lunch (let's say Splash, Indy, Roger Rabbit, Space, Buzz). After lunch you definitely could get them for Big Thunder and Star Tours, and probably Indy, but Space and Splash run out fairly early.
As others have said, you can get more if DL isn't crowded, but then you wouldn't need them.