I changed the front brake rotors and now the pedal feels soft and then you have to pump it to stop.   I have changed brakes many times and did this one the same way.   I pushed in the calipers with a c-clamp, removed rotors and pads.  Then,  I put new parts on and bolted it back together.  I pumped the brakes a couple of times until the pedal was firm, but now the pedal feels soft and the will get firm if you pump it once.

   I did not open the system to allow air to enter.  So I don't think that I need to bleed them.  Do you think that I could have accidentally installed something wrong, like, a pad isn't sitting right or something?

I feel frustrated, because it is a job that I have done countless times and never had a problem like this.  I am taking it apart today to see if I can figure it out.  There are countless hits for this problem when I google it, but nobody has a real answer for it.

I have found several causes of symptoms like yours, bent hub, sticking slider pins, reuse of old pad hardware etc.

Bleed the brakes.  It is time to get rid of the old brake fluid anyway. 
You may have shoved some gunk back into the check valve when you compressed the calipers.  (That is the way I do it also.)

Bleed the brakes.  It is time to get rid of the old brake fluid anyway. 
You may have shoved some gunk back into the check valve when you compressed the calipers.  (That is the way I do it also.)

Yep, I agree.  If the brake fluid is dark color, then it should be changed.  The brake fluid should be clear.  Just bleed the brakes until the reservoir is about empty (don't let it get completely empty, otherwise you'll have to bleed the master cylinder).  Then fill the reservoir, pump the brakes to push the old fluid out (I'd start with the bleeder valve farthest from the reservoir).  Keep refilling and pumping, until you get clear fluid out of each bleeder valve.  Then top off the reservoir.

Did you check the rotors for run-out after installing them?  It's possible for new rotors to exhibit run-out and this will cuase them to push the pistons back into the calipers as they rotate, and then when you step on the brake you chave to pump to move the pistons out enough to stop the vehicle.

Some of the causes of run-out are warped rotors or a dirty mounting face between the rotor and the hub.

Another possible cause (as talonxracer has pointed out) is binding caliper slides

Great suggestions......

I prefer old rotors turned (if within spec) to some of
those cheap imported ones. Turned used rotors run
truer IMO.

But agreed, flush brake fluid and lubricate slides.

I agree with checking the sliders.  Did mine, acted the same, rechecked and lubricated the sliders and it worked for me.

Great suggestions......

I prefer old rotors turned (if within spec) to some of
those cheap imported ones. Turned used rotors run
truer IMO.

But agreed, flush brake fluid and lubricate slides.

If you're going to buy cheap, then expect cheap - you can however get decent quality inexpensively.  I'm running Brembo rotors on one of my Suzukis - $35 a piece - and those went on after I turned the in spec. OE rotors, which promptly warped on me.
I'd take a decent replacement over a turned used rotor any day of the week

Instead of pushing all the old fluid out through the system suck all the old fluid out of the reservoirs refill with new then bleed