Why do we keep trotting out 2001?
The Discovery is the most realistic? PAH!
Where exactly did the crew plan on surviving a solar flare? Why put the fragile crew module at the front where it can get more impacts from interplanetary dust & particles? Lets not forget the massive picture window 'cockpit' - why would it need such a cockpit? Apollo flew to the moon without the need for windows! How the hell did it cope with the massive torque of the spinning hab section? If the film was all about realism, and used the spinning hab section to provide Coriolis force 'gravity', how the hell did they get 'gravity' in the pod bay? Did anyone think about the massive osmotic imbalance you'd get from the limited diameter hab module anyway?(15m or so? Force gradient strong enough to do something horrid to your cardiovascular system!) Where was the counterbalance required to stop the whole ship pinwheeling? The Discovery is wrong wrong wrong on so many counts... yet everyone raves about it. Bloody hell, read some engineering! I think only Kubrick would have said 'the most realistic ever'; he sure had tickets on himself!
Better realism - the 'Mars 1' from Mission to Mars - also highlighted some of the dangers of interplanetary dust particles
'Icarus 2' from 'Sunshine'
And yes, the starship that was onscreen for all of about 8 seconds in Avatar was awesomely well thought through. The VSTOL 'Shuttles' were also nice, as were the nifty little rotor-wings.
The unnamed starship from 'The Fountain' for its sheer preposterous whimsy - and a massive tip of the hat to E.E. Doc Smith's 'Skylark'
The 'Rama' starships from Arthur C Clarke's 'Rama' series are pretty good ideas for generation ships.
While the series wasn't up to scratch, the ships from 'Space:1999' were quite well thought out.
More novels - Stephen Baxter's 'voyage' and 'Titan' both describe in excruciating detail interplanetary craft based on the Apollo Venus flyby plans (real, look it up) and a somewhat more precarious but still possibly doable Shuttle-to-Titan.
Another one from books - the 'Ares' from Kim Stanley Robinson's massive Mars trilogy was also based on Shuttle-tech.
As for most-realistic starships of any space-faring species, I don't think you can go past the delightfully eccentric 'living' starships of The Culture series by Iain M Banks. Give me a GSV or a Fast Picket any day!