Aristotle is credited with classifying our senses into five, and to these days schoolchildren are taught we have five senses. Yet five is but a small subset of our senses.

To answer this question, we first need a definition of whose senses we are counting, and what we mean by a sense. 

You could count any animal sense, or just people's. It'll be hard enough to reach agreement w/people, so I'd stick with that, as I'm quite certain that a full compendium of the senses of all living species has yet to be compiled. 

Wikipedia http://en.wikipedia.org/wiki/The_Senses defines a sense as "A system that consists of a group of sensory cell types that responds to a specific physical phenomenon, and that corresponds to a particular group of regions within the brain where the signals are received and interpreted." Yet additional clarity is needed to decide, for example, if each of the 4 types of photoreceptors constitutes one sense or if all 4 are considered one sense. Ultimately, the counting of senses is rather subjective, as, for example, the thousands of different olfactory receptor types go to different parts of the brain and are responsible for the perception of different specific phenomena, and yet are typically lumped into one sense because of the many similarities between them. That said, there are differences between receptors whose axons are carried by the trigeminal nerve and others, so even if you did want to lump, there is more than one sense in the nose.

Ultimately, our perception is made by the brain based on the activity of billions of neurons, and each of these neurons is somewhat unique given not just its gene expression profile but its connectivity pattern with thousands of other neurons, so any simple classification into senses is likely to be rather simplistic or subjective. Which doesn't mean that it's not interesting to count nonetheless.

The list the article gives is probably still incomplete, but includes: sight, hearing, touch, smell and taste,nociception (pain, and there is more than one kind of these); equilibrioception (balance); proprioception and kinaesthesia (joint motion (not sure why list this separately from the internal senses below) and acceleration); sense of time (which doesn't fall into the definition above in that there isn't, to my knowledge, a single specialized kind of receptors involved, so I would exclude it from this list); thermoception (which is really two separate senses of heat and cold perception), plus a plethora of internal senses:

Pulmonary stretch receptors are found in the lungs and control the respiratory rate.

The chemoreceptor trigger zone is an area of the medulla in the brain that receives inputs from blood-borne drugs or hormones, and communicates with the vomiting center.

Cutaneous receptors in the skin not only respond to touch, pressure, and temperature, but also respond to vasodilation in the skin such as blushing.

Stretch receptors in the gastrointestinal tract sense gas distension that may result in colic pain.

Stimulation of sensory receptors in the esophagus result in sensations felt in the throat when swallowing, vomiting, or during acid reflux.

Sensory receptors in pharynx mucosa, similar to touch receptors in the skin, sense foreign objects such as food that may result in a gag reflex and corresponding gagging sensation.

Stimulation of sensory receptors in the urinary bladder and rectum may result in sensations of fullness.

Stimulation of stretch sensors that sense dilation of various blood vessels may result in pain, for example headache caused by vasodilation of brain arteries.

 I'm surprised that the article did not list any sexual sense, as we certainly have both specialized receptors and sensations involved in sexual perception. You may choose to just call them touch, but if you have never perceived the difference between sexual stimulation of your clit or penis and touch of the rest of your body, I suggest you get out (or in) more. Where a unique sensation can arise only of stimulation of a particular part of the body, specialized cells must exist.

There are other senses still, and they vary from person to person: I get a tingling in my tongue from hot and sour soup, and I get sensations in my gut from Chinese hot food I have only found in China that no other stimulus has ever elicited.

I suspect when neurons have all been catalogued in their excruciating variety and detail, many more senses will become apparent; the diversity of human percepts related to the senses is of course much larger than the above --suffice it to name tickling, which is also not distributed uniformly across the body.

Magnetic sense does not seem to be one of the human senses, as the only reports have been irreproducible by the scientific community at large.