It was posted on this message board before, try doing a search.

This is all I could find:

Can Superman really move planets?

and

When Superboy moved a solar system by dragging it on a chain

but very few actual stories were mentioned.

One that comes to mind is actually somewhat recent:  In one of Grant Morrison's JLA issues, Electro-Superman-Blue moved the Earth's moon.  (Proof that with a good writer, even a bad idea can be turned into something really cool.)

Here's a definite "planet-moving" story. In Superman #220 (October 1969), Supes moved the Earth out of the path of an alien seed that was going to burrow into the core and take over the planet. See cover here: http://www.comics.org/coverview.lasso?id=23014&zoom=4

Here's a case where the cover appears to show "planet-moving", but the story is . . . even weirder. In World's Finest Comics #208 (December 1971), Dr. Fate gives Superman mystical chains to pull the Earth's (Earth-Two's, actually) continents apart after some aliens speed-up the movement of the tectonic plates. See cover here: http://www.comics.org/coverview.lasso?id=24699&zoom=4

Additional postscript. I used to keep notes on the outer limtis of the Silver Age Superman's powers---the fastest he's ever gone, the most he's ever lifted, etc. If I find them, I'll post them here.

I remember I DID find something indicating a reasonable upper limit to Superman's speed...and I remember it was something as mind-boggling as the 6.6 sextillion-ton limit on his strength. (I think one prelimiary thing was the span of the Milky Way, since Flash and Superman, in their second race, raced across the Milky Way, and I assumed a maximum of eight hours for the race, or else Barry Allen and/or Clark Kent would have had questions to answer for when they couldn't show up for work the next morning. Since we're 30,000 light years from the center of the Milky Way, and the whole Milky Way galaxy is 100,000 light years across, that would be a speed (in defiance of Einstein) of at least 7,777 light years PER HOUR. I want to say I found something ELSE that indicated an even greater speed.) Let me see if I can find my notes.

--Al
PS. Checking the description, the race was to the edge of the galaxy and back---20,000 light years there, and another 20,000 back. That would come out ---assuming it happened in under eight hours, a good assumption, since the whole Justice League was frozen, and even on the weekend, you would think SOMEONE would have to get back to work pretty soon---to 5000 light years an hour.
   That's for Superman AND Flash...by the way...
   That's pretty fast. That's....let's see....
   43,800,000 times c, times the speed of light. Almost 44 million times the speed of light.
   Of course, that's an AVERAGE of their speed. They might have to spend some time accelerating to that speed, which would mean their top speed was even higher...
    But at that speed, you could get to Rann---to Alpha Centauri...in three seconds.
   You could reach Thanagar, around Polaris, 430 light years from us, in a little over five minutes.
   On the other hand, as fast as it is, when you get into intergalactic distances, it's still a stretch. The Andromeda galaxy---the nearest galaxy to us--- is 16-17 days away at that speed. To reach where the nearest quasar is---or was, since we see light after it reaches us---1 billion light years from us---would take over 22 YEARS.
   Even at the Silver Age Superman's speed, it's a big, big universe.