Samsung patents against Apple - zero. And Samsung was just turned down by the Dutch court in their patent infringement case today..
Actually, thats not really true.
Samsung DOES hold quite a few patents that are, presently, being infringed by Apple's iPhone.
The thing that seems difficult for a lot of people to understand is the fact that not all patents are the same, or can be treated the same way in cases like this. And, its also worth noting that (generally speaking) Samsung's patents come in different areas of technology than do Apple's.
Most of the Patents held by Samsung (in the cases we're talking about here) are what are known as Standards-Essential or "FRAND" patents related to mobile telephone systems. What is this?
Basically, when a new industry - such as the mobile phone business - gets started, it is very important that all the participants (handset manufacturers, carriers, backhaul providers, antenna mast installers, etc.) work on the same standards. If they DIDN'T, then a handset made by company A, would work with infrastructure installed by company B. It would be very inefficient, you'd end up with dozens of redundant networks, etc.
So what generally happens is that Industry Groups, referred to as Standards Setting Organizations (SSOs) agree on a single standard for things like the encryption and communication protocols. These are typically the product of a single company - and are patented by that company.
Now, in exchange for giving that company a pure monopoly, the SSO expects that those patents be considered FRAND-encumbered. FRAND is an acronym for "Fair, Reasonable, and Non-Discriminatory" - and it really means that a) the patent holder MUST license it to all qualified buyers. It cannot refuse to license it to a competitor. And it has to license it under "reasonable" terms.
Now, that doesn't mean it has to license its technology to everyone at exactly the same price. A buyer who wants a lciense for two million handsets, for instance, would pay a much lower unit royalty, than someone who only wanted fifty thousand.
Obviously, there aren't hard rules under this standard. And often license terms are the result of intense negotiation, and sometimes result in litigation.
Again: Virtually ALL of the patents Samsung is alleging Apple infringes are FRAND-encumbered. That's because Samsung happened to be a big chip maker at the time when cellphone standards worldwide came into being. But again, remember that Samsung is OBLIGED to license that technology to Apple - and they can't demand unreasonable payment for it.
By way of contrast, the Patents that Apple holds are most definitely NOT FRAND-encumbered. They relate to things like the way the user interacts with the phone, and are not "Standards Essential."