So, I think perhaps hysteria over the nuclear plant issue is getting a little out of hand in some places. Some people are leaving Tokyo - even leaving the country - over the fear of radiation. And I just recently read that the Swedish nuclear authority has been getting hundreds of calls from people worried about the effect of fallout in Sweden. Which is not ridiculous since people's fears are very real, and fear needs to be taken seriously, but the fear is misplaced and uninformed.
First, and most important, we have tens of thousands of people dead in Tohoku, and many tens of thousands still in dire need of assistance. People still miss basic shelter and water in many areas. This is the real disaster, far worse than any effect of a broken-down reactor. The nuclear thing is a noisy sideshow, nothing more.
Leaving Tokyo: Good idea - but not for the situation at Fukushima. The Tokyo area has rolling blackouts, disrupted communications and a lack of supplies, as both power and other resources are funnelled to the disaster-stricken areas. Chances are your workplace or your school is shut down anyhow, and your company may be shifting operations to branch offices out west for the time being. If you can visit relatives in Kansai or Kyushu for a few weeks that may help relieve stress in the Kanto area a little bit, not to mention relieve some stress for yourself.
Radiation: First, to be absolutely clear, I'm not an expert. I am a researcher, but not in radiomedicine, not in nuclear engineering and not in anything connected to it. Don't take my word for things - but don't take the word of other people without expertise either.
"Sievert" is a measure of a dose of radiation, like liter or cups for liquid, meter for lengths or kilogram for weights. Sievert per hour tells you the rate over time - like kilometers per hour for speed. I'll give all numbers below in the same unit, microsievert per hour (shortened uSV/h).
Peak radiation at the Fukushima I plant have been high, well into medically unsafe levels. It is truly dangerous for the workers at the plant, and people in the area have been evacuated for good reason. But the strength quickly diminishes with distance.
Highest measured radiation so far in Ibaraki prefecture, near Fukushima was 5 microsievert (uSv) per hour. Tochigi, halfway between Tokyo and Fukushima has had a peak of 1.3 uSv/h. In Tokyo the peak was 0.8 uSv/h. All these quickly dropped to near normal again. Note how the peak is lower the further away the place is. Here in Osaka there was never any detectable difference. Sweden will never see any effect from this accident at all.
Here is a live radiation counter in Tokyo. At the time of writing, you can see a slow hump of activity over last night and morning, on average around 0.1 uSv and at most 0.2 uSv/h more than usual (100 cpm is very roughly 1 uSv/h), but back to near normal again. The lower graph is the typical level.
Normal total background radiation ranges from 0.15 to 0.5 uSV/h. Exactly how much depends on where you live - Scandinavia, for instance, tends to have relatively high background radiation, with about 0.45 microsievert per hour, and there are some places in high mountain areas that naturally give you over 5 uSv/h. Tokyo, on the other hand, lies at the lower end of the range, as you can see at the link above.
Flying exposes you to more cosmic radiation, simply because you're above much of the atmosphere. While you're chewing on a rubbery chicken and watching last years hit movie on a grainy monitor you're getting about 7 uSv every hour, more than the peak value in Ibaraki.
Let's say you decide it's a good time to escape home to Sweden. The entire peak gave you around 1 uSv extra radiation, the nightly hump also totals around 1 uSv (an average of 0.1 uSv for ten hours). The constant background level in Tokyo is about 0.2 uSv/h now. You want to leave Tokyo and get home to safe, dependable Stockholm. You hop on the airplane, which gives you about 75 uSv during the trip - 75 times the peak, and 75 times the slow hump last night - and arrive in Sweden.
Sweden has a constant background radiation rate at 0.45 uSv/h - more than twice what you have in Tokyo, and higher than during that hump of activity last night. If you live in an old stone house the rate is higher still. So, leaving Tokyo for Sweden means increasing your radiation exposure, not decreasing it.
This doesn't matter, of course, as all these values are far below any unsafe levels. What is unsafe? Around 100 000 microsievert over a year - that is 11 uSv/h for a year. Occupational limits are about 2.2 uSv/h for a year, but that's work-related exposure over and above any other sources. At about 0.2 uSv/h in Tokyo you'd need five times that level to reach workplace limits and up to fifty times current levels for a whole year to get into real unsafe territory.