I don't know what to suggest, and will be watching this post for my own situation.

Start viewing late night tv informercials or search "leather mending" in google and you'll get the idea. There is a plastic product offered periodically that "mends" leather. You mix a colored resin to closely match the color of your sofa, dab it on and let it dry. Stuff's been around for years. I've never had to use it but it seems pretty straightforward.

OR

If you can steal a small area of leather from underneath the sofa you can have a professional upholstery shop that specializes in leather come out to your house. They basically steal a tiny square of leather, enlarge the hole, force the square into the hole, dab high powered leather glue to affix it, sand it down to an even height (somewhat), then dye the area to match your sofa. It shouldn't be too pricey, say $150-200.

That being said, until you get it fixed, you'll need to stop putting pressure on the section that has the puncture to avoid opening the hole any further.

For the future, can you clip your dog's nails? Or get a sturdy, plainweave linen throw to act as a doggie blanket.

There are products to repair this. Check with a local upholstery or leather goods shop. We have a local shop that stores furs in the summer and they also care for leather apparel; including doing repairs.

My dogs did this .... X3. Two where rips and one was a quarter sized whole of which I was lucky to find the ripped out piece. I looked at doing those 'as seen on tv spots' but they all had bad reviews and none offered the color matching I wanted. My sofa isn't black and isnt brown. I also called upholstery places and for the life of me I couldn't find anyone short of paying hundreds of dollars. I ended up using 3-0 silk suture material on an arched needle, the kind used for stitches. It may not be something you have access to but it's strong and lasting. It's definitely not invisible ( if not slightly charming) but I'm sure the dogs will give this all a go again.

Sewing it is probably the least expensive and most durable. You can also get "designer vinyl tape" in different colors at the hardware store and just put a piece of that over it. It's not invisible, but it stops the hole from getting bigger.

There are vinyl and leather repair people who specialize in this sort of thing:

www.precisionleathertuning.com
www.vinylpro.com
www.leathervinylmd.com

Those are just a few.

This happened to my couch, too. I removed the cover, and reinforced the underside of the rip with good ole' duct tape. Its held up well so far.

Dora the Explorer band-aid.

turn the cushion over

Love you Raina!

Put a leather patch on the inside using Tear Mender Adhesive. It's an 'as seen on TV' product but it really works well - it creates this flexible rubber bond. I have found it in hardware stores, but here's a link to it on amazon:
http://www.amazon.com/Tear-Mender-Instant-Leather-Adhesive-2/dp/B000BQKGR0

Depends on how "hidden" you want the repair to be. The only way it will ever appear as though the tear never happened is to have an upholsterer replace the panel of leather that contains the hole. If you're ok with allowing your furniture to wear the faded battle scars of its life then many of the methods mentioned above could be sufficient.

Leather repair kits can be purchased in an auto supply store.

My favorite would be to patch it from behind, with sewing it closed taking a close second. You can buy curved needles at most crafty shops.

If none of the above work, or if you don't want to see the tear...

You may have a sample of your leather's dye-lot on the bottom of your sofa. If you do, its for situations like this. You may be able to go back to where ever you bought the sofa, and go through them to work with the sofa company. They may be able to send you a new panel in the same leather type to replace the damaged one. If you're lucky, they may even still have some of the same dye-lot that was used on your sofa. Some companies will let you ship the entire cushion and they'll replace the panel, or some will simply send you the new panel, in which case you'll need a leather upholsterer.

If the store isn't interested in working with you on this (which would be lazy on their part - it really only takes a phone call or two), you may be able to call the furniture company itself.

Good luck!

Can someone identify the source of the small picture of the leather couches at the beginning of this post?

http://www.leatherrepairkits.com/repair_kit.shtml

http://www.asseenontvguys.com/leather-repair-kit.aspx

http://www.bing.com/search?q=leather+repair+kit&src=IE-SearchBox

I'm a furniture repair technician for Furniture Medic, my family's business. we repair this sort of thing all the time (I actually just did a leather rip today). Unfortunately we're located in Chicago, but call the Furniture Medic headquarters to see if there is a franchise in your area. If not, your best bet is to patch it from underneath with a similar matching scrap of leather. We use a special adhesive that can be molded to match the leather grain then color match with dye.

Try a mobile auto upholstery service, we had them come to the car lot all the time.

Completely side-tracked by the photo of the actual damage. I love it! Would be a fantastic piece of abstract art if framed. Dark, moody, a bit questionable as to subject. Mind if I steal it? (No joke!)

Much obliged for all this wonderful advice - this is why the AT community is such a fabulous resource!
We've started with the Dora the Explorer band aid (he, he) and will begin searching for leather repair technicians in our area. The idea of suturing the rip is really quite appealing, especially the thought of using a hot pink thread... why not embrace the chaos? With toddlers and dogs, why shouldn't both my life and my furniture look weathered and and a bit world-weary?!

Hvg001 - the source of the top pic is my living room, where the original crime was committed... the matchy-matchy sofa, ottoman and chair are (embarrassingly!) from a department store that has now gone under. The bookshelves are shamelessly borrowed from this AT post:
http://www.apartmenttherapy.com/chicago/house-tours/house-tour-shannon-and-emmetts-from-factory-to-family-007338

And to BreathingRooms, feel free to use my sad, torn little image in your conceptual art piece. It's quite low resolution, but I can email you a higher res pic if you're compelled by it!

Once again, thanks for all the stellar advice!

i know I'm probably two years too late for you but i checked out this site for advice when my cat ripped my new leather sofa and then ended up finding a sort of furniture band-aid called mastaplasta. so easy. i got a brown red leather sofa but got a brown crown mastaplasta and it looks like an expensive makers label on my sofa and not like i'm hiding anything. The rip was on the side not the seat though. I probably should have got a red one but i was feeling as wild as my cat at the time. It's cool and really easy for anyone like me who doesn't want to work too hard. I just got it on amazon and felt it was worth spreading the word. You can get plain ones or other designs. Anyway it might still help anyone just looking now...