How many Tapcons should be used to anchor a baseplate to a concrete floor?

If you've prebuilt the wall, one per stud bay will provide sufficient clamping. (6 total for 16inch stud spacing)

If you are stick-building in place , I like two at each end (staggered by an inch and countersunk). Then 3 more at 2 ft intervals. (7 total for 16inch stud spacing)

I use the 1/4 inch vs the 3/16 version for more strength. The 3 1/2 x 1/4 are good for this task.

I'm doing something similar, except I'm using powder-actuated charges to push a nail in instead of a Tapcon scheme.

Same situation in the basement, too... non-load-bearing regular partition walls, with kids running around and all that.

See my earlier question here: Is there a recommended distance between fasteners on sole plates?

In short, I'm using 3 fasteners, though that looks to be more than what's necessary.

My rule of thumb is one at each end, and then every other stud. Every other stud may be overkill, but it's easier to overdue it a little than under do it and have to repair the job later. Structural fasteners around the top and bottom plates tends to be done as close to a stud as possible, to leave lots of room for utilities that are being drilled through. You won't have this on your concrete floor, but it doesn't hurt to stay close to the stud (but not so close that you can't fit your drill in).

The sill or bottom plate you are securing to the concrete will likely not take any impact itself, but will have to accept impacts from studs attached to it.

This question shows a typical 2x4 can expect to hold well over 300 pounds of evenly distributed force over a 6 foot span with no issues. It will handle sudden impacts of significantly greater magnitude before failing. So you can expect the wood to be fine with only 3 positions along it secured to the floor.

A 3/16 tapcon, embedded in normal concrete one inch deep has a sheer strength of over 700 pounds.

So as far as "long lasting stability" three tapcons per 8 foot length is probably still overkill.

You might want to secure it more frequently for purposes of vibration/noise reduction, or if your concrete is suspect, but beyond that you're wasting fasteners, drill bits, and time.

I have been framing basement walls for years. I use 3 tapcon anchors per 8 ft run. Pre drill the treated base plate for the anchors, counter sink them a 1/4 inch, then lay a heavy bead of construction adhesive under the plate. Use a good concrete bit to drill the anchor holes. They should be at least an inch deep. I nail up my framing on the basement floor and then stand it up on the base plate and nail in place. The ram set method may be somewhat quicker but leaves a tail sticking up.