Disclaimer: The viewpoint expressed below is from a graduate student studying mechanical engineering, in a Mechanical, Aerospace, & Nuclear department where many of the department seminars/colloquiums are on nuclear topics. As such it is biased towards scientific reasoning and facts that I have read in peer-reviewed journals or have seen in presentations by people with Ph.D.s on the topic, instead of media-led FUD.
While there are still significant issues to overcome when it comes to building new nuke plants, at this point the largest hurdle is waste and not reactor safety. Why? Because there have been 2 or more generations (depending on how you count them) of plant designs since the GE reactors at Fukushima Daiichi were built. Each with new safety features, and you'd better believe any future plant will learn from what has happened there over the past month. People seem to forget very soon the 3 Mile Island incident just outside Harrisburg PA, which was the worst nuclear disaster ever in the United States. How bad was it? Well, radiation levels around the reactor went up and and are still as high as ... the same as background levels anywhere else in the country, within a noise margin. That's because the plant was designed with safeguards, and as soon as something happened they went into effect. If you look for valid scientific sources about what is going on in Japan right now, it seems like the current knowledge is that the plants were either designed for a "worse case" scenario of a lower magnitude earthquake, or didn't anticipate the (inevitable) tsunami that happens when there's an earthquake on an island. What this means is that future plants will be built with an even larger safety margin and be more expensive, but that is the price to pay for clean, reliable energy.
There are already full plans for single fuel load reactors that don't ever require new rods and will run for their entire lifetime on an initial load, also reacting the fuel to a lower energy state than current designs, leaving the waste with a half-life an order of magnitude shorter than existing reactors. This also means lower temperatures in waste ponds (or no ponds at all until the plant is decommissioned). Unfortunately the time it takes to go from a proposal to a working new plant is on the order of 10 years, in the US at least. Maybe when all the current plants go down and aren't replaced, people will start to realize that they're just afraid of things they don't understand, and possibly learn to accept that "I don't understand it!" does not mean "Nobody understands it, and it's gonna kill me!"
On the flip side, it is also true that if the entire world were to switch to nuclear energy right now, there wouldn't be enough Uranium to go around, but it's still a darn sight better than the current state of petroleum based fuels. And many reports are saying that methane (natural gas) powered plants are a "sustainable" alternative, and current advances in filtration and sequestration make coal plants another short term option that are both more environmentally friendly than many existing gas fueled plants.
So for all the people who say "No nukes, NIMBY!", what DO you propose? If we don't build more of them, we're either going to harm the environment even more with coal/methane/petroleum plants, or run out of power. There isn't enough combined wind, solar, and hydro power available in the continental United States to power the current electricity usage. Period. Even if every square foot of land was covered in one or more of those collection methods. Either we build more nukes, build more smog plants, or drastically decrease usage, with the last option being the best but hilarious if you think it will happen without an even bigger disaster sparking it.