We know from the nuclear power industry that spent fuel storage pools are pretty safe places to be around, radiation-wise. They're actually safe to swim in, to a point, because they're serviced routinely by human divers.
So, water is a really good radiation shield. How good? Well, according to a report on the topic prepared for the DoE back in 1977, a layer of water 7 centimeters thick reduces the ionizing radiation (rays and particles) transmitted through it by half (the remainder is captured or moderated to non-ionizing energy levels, mainly heat). Freshly discharged nuclear fuel puts out about 100,000 R/hour as measured from one foot away in air (at that rate, certain death is about 5 minutes' exposure and you'd fall into a coma in about 10). Background ionizing radiation levels on Earth's surface are about .000001 R/hour (1 mSv/hr), while a "safe dose" to live with long-term is about .0004 R/hr. A halving represents about .3 powers of 10, so in rough terms, to reduce a fresh fuel rod's radioactivity to safe levels, you would need about 2 meters, and through more than 2.5m the radioactivity of the fuel rods is indistinguishable from background radiation.
According to Wikipedia, the upper estimate for a dose equivalent received by unshielded astronauts operating outside Earth's magnetic field (such as a mission to Mars) is about 90,000 R/yr or about 10 R/hour. If we assume the energy levels are comparable, reducing that to lower than Earth background radiation would only require a layer of water around 1 meter thick.
However, let's do some more math. Let's say that the Mars vehicle that will get them there and back is a cylinder roughly 3.5m by 20m (same as was used for the MARS-500 experiments). With 1m of shielding water around all surfaces of that cylinder, the outer hull would be about 4.5m by 22m. The volume of shielding water needed is the difference between those two cylinders, or 22π(4.52) - 20π(3.52) ~= 630m3. As one cubic meter of water weighs 1 metric ton (1,000kg), that's 630,000kg to get into space.
Putting that in perspective, the current record holder for payload-to-LEO is the Saturn V rocket, which had a maximum LEO payload of 120,000kg (that being the S-IVB for most of its missions). To put the volume of water we'd need into orbit would require 6 Saturn V rockets. The planned-but-never-built Ares V was spec'ed to have 188kg P2LEO capacity, which would have cut down the number of launches to only 3. Doing it with Space Shuttles would take 25 misisons. Doing it with any orbital rocket currently in service, manned or unmanned (Soyuz II, Soyuz FG, Delta IV, Atlas V, Falcon IX) would require hundreds of them.