When the apples start falling, it means you should pick them if you already haven't. Since you don't know the variety, make note of the date they start to fall. Then, next year, start testing them a couple of weeks before. Lift up on the stem, and a ripe apple will come off in your hand.

Alternatively, you can pick one and check the seeds - when they turn entirely dark, the apple is ripe to eat.

Depending on the variety, some apples are best when picked early, some improve when left on the tree - but not so long they get soft and mealy. Some improve in refrigerated storage. You'll have to experiment.

Maybe if you post a photo, someone here will recognize your apple.

Thanks, ltilton! Here are some photos I just took. I'd describe these apples as being sweet w/ a bit of tartness. Very crisp! excellent for fresh eating but I'm pretty sure they'd be good for baking too. they're juicy, and the flesh is a bit yellow... definitely not what I'd call white flesh.

Of course they haven't been "cared for" -- I searched today and believe the spotting on the skin is sooty blotch. Many have deep cracks near the base of the stem... I assume that these problems were primarily caused by the excessive rain we had this spring, summer, and autumn! :p

Any thoughts on what variety these apples might be? and of course, whether they should be picked immediately?

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Not all apple varieties are ready to completely harvest when a few have fallen. There is quite a range between varieties as far as the length of harvest time. For apples I plan to eat within the next couple of months I usually only pick them when they cleanly separate at the stem with a slight twist and the background color has turned from green to yellow. Varieties that aren't world class keepers I pick a bit green for longer storage.

Of course, if a variety is already mushy when it fits the before mentioned criteria next time around you should pick it green. All varieties are at least slightly different regarding harvest issues.