Here's a little more on the chances that the methane is produced by the breakdown of organics that come to the surface of Mars from space. On the back of my envelope, 10 parts per billion in the martian atmosphere looks like about 90,000 tonnes of methane. If methane lasts for three centuries in the martian atmosphere, then keeping 90,000 tonnes in the atmosphere means adding about 300 tonnes a year. That's a very rough estimate, but probably in the right sort of ballpark, to an order of magnitude. More than 30 tonnes, less than 3,000.
The best estimate I've been able to find of the rate at which organic material (meaning carbon bearing molecules) arrives at the surface of Mars is in a 1996 paper by George Flynn of SUNY-Plattsburgh. ("The delivery of organic matter from asteroids and comets to the early surface of Mars", Earth, Moon and Planets 72 469-474 -- not as far as I can see available online.) Most of the material that falls to Mars from space is in the form of little dust particles; based on the flux of these particles measured on earth, Flynn estimates that today the average amount of matter delivered this way is 8,600 tonnes a year. Some of that material will be heated up so much as it comes through the atmosphere that any organic molecules in it will be destroyed, but at least 2,400 tonnes a year should make it to the surface without having its organic matter blow-torched away. The amount of this dust made up of organic molecules is a subject of some debate, as I understand it; Flynn goes with 10%, which is apparently fairly mainstream. Thus he suggests that the amount of unaltered organic matter arriving on the Martian surface each year is about 240 tonnes.
(A neat aside from the Flynn paper: over the course of Mars's history 240 tonnes a year would add up to a trillion tonnes of carbon, which is roughly as much as is found in the earth's entire biosphere. This doesn't mean 240 tonnes a year is a lot -- it means that the planet is really incredibly old.)
If my calculations above are correct, a dustfall of 240 tonnes a year means that that organic matter would have to be converted into methane really very efficiently -- yields of between 10% and 100% -- if that dust were the source. That sort of yield sounds unlikely. But it seems undeniable that something happens to those organic molecules -- because when the Viking landers looked for organics in the martian soil that dust lands on, they found nothing. That's one of the reasons why, when one of the life detection experiments showed a life-like chemical response from the soil, it was discounted -- life in soil that has no measurable level of organic compounds in it seems highly unlikely. For an account of all this, see the section on Viking in Michael Caplinger's article here; for Gil Levin's minority view that life was detected, have a look here. (Technically, by the way, the stuff on the surface of Mars is regolith, not soil, since "soil" carries connotations of the possibility of growth, the presence of nutrients, etc. This is a technicality I am currently ignoring.)
The mainstream answer to what happens to the organic material is that it gets oxidised in some way by chemicals in the soil. (This is taken to explain the "life-like" response of the soil in that Viking experiment; fed with organic molecules the soil produced carbon dioxide, just as a lifeform would.) Oxidation is not something that produces methane, though I suppose it's conceivable that secondary reactions might produce a little. Another possibility is that the organics are smashed apart by ultraviolet light, with no need for weird soil chemistry. Experiments by Carol Stoker at NASA Ames seem to show that the harsh ultraviolet at the martian surface would be able to destroy organics at a rate that vastly exceeds that at which they could fall from the sky (abstract here). I don't know much about photochemistry, but it seems highly unlikely that this process would have methane as a primary product. Where would the necessary hydrogen come from? (See update below)
Another possibility is that the organics are not destroyed, but that instead they are converted chemically into a form sufficiently inert that it could not be detected by the Vikings' Gas Chromatograph Mass Spectrometer instruments (a spare part for which, incidentally, I was once shown by Jim Lovelock in his workshop -- it was one of the experiments he worked on when consulting with NASA). This is an intriguing idea, expounded by the wonderfully imaginative biochemist Steven Benner in an article in the proceedings of the National Academy of Sciences a couple of years ago (abstract here with link to full text). This possibility is undoubtedly interesting -- but Benner says it wouldn't give off methane.
So at the moment, it seems to me, the chances of the methane being made from stuff that comes to Mars from elsewhere looks pretty slim.
Presswatch: This story has now (Monday evening) been dealt with by much of the mainstream media in the UK, including the BBC. The PA wire service has a story that's been picked up by a number of papers; it includes the opinion of Colin Pillinger, who "said the discovery could be evidence of 'past life or even current life'. He said he believed the gas was unlikely to be the production of volcanic activity alone." There's a nice account at New Scientist that covers all the bases. In all honesty, though, there's not much out there that's not also here (though I'll admit other people are being more concise...) As far as I can see, the American press has yet to chime in, though Slashdot is on the case.
UPDATE: I've now managed to get a copy of the paper on Carol Stoker's experiments ("Organic degradation under simulated martian conditions", Carol R. Stoker and Mark A. Bullock, JGR 102 E5, pages 10,881 to 10,888 -- thanks Kara!) and it shows that, as I said, I don't know much about photochemistry. In fact there is methane given off as a primary product. This doesn't necessarily mean that's actually happening on Mars, though, certainly not at the rate necessary to explain the methane measurements. For one thing some or all of the breaking down of organics may be done by soil chemicals, not ultraviolet light. For another the organics in meteoritic dust are more graphite-like than the glycine used in the experimental set up, which might make a difference. As Carol and Mark Bullock point out, some of the organics might be tough enough neither to be knocked to pieces by ultraviolet light nor to be picked up by the Viking GCMS. Still, it's important to note that this is an abiogenic mechanism that might be producing some methane out of some of the stuff that falls from the sky.