The stars would turn blue ahead and red behind as the ship speeded up.

Very quickly the light would be shifted out of our range. Maybe long-wave energy would be accelerated into visible frequencies with increased speed.

Nothing should be visible at multiple light speeds. Hope the front shields are on. Imagine hitting a speck of dust.

Depictions of translight spaceflight are very difficult, mainly because there are several different methods of achieving it, each with different visual effects which the traveller will see. I'll go through a few of the most typically discussed in SF, along with their scientific backing (at least as far as modern physics permits) along with a Star Trek comparison, where possible.

• Alcubierre Drive - the Warp Drive
• In the 1990's Miguel Alcubierre worked out that the mathematics permitting the design of a trans-light drive , through field encapsulation of a vessel in its own bubble of space time, was not impossible. This not unnaturally caused quite a stir, and since that time, Alcubierre is often mentioned in the Star Trek world as the primary influence of the fictional future Dr. Zefram Cochrane, who invents that story's warp drive. The Alcubierre Drive encapsulates a vessel in a pocket of space time, isolated from the rest of the universe - Star Trek fans will recognise this concept as a Warp Field. The pocket can be manipulated in such a way as to produce relative thrust in the outer universe, but as it is not really interacting with the universe, it would not suffer the effects of Lorentz-Fitzgerald Time Dilation at trans-luminal speeds. In addition, time within the bubble would continue at the same rate as time outside of the bubble, no matter at what speed the bubble containing the ship would appear to move. Moving the ship will require creating a virtual white hole behind the ship,a nd a virtual black hole in front, in order to provide a thrust force - literally a cosmic jet engine.Creating such a bubble is not yet fully understood - Alubierre, in his paper, indicated that negative energy would be required to create such a bubble. Seeing as modern physicists have enough trouble with positive energy, and can't even create that, negative energy and the bubble remain tanatalising possibilities, and thank goodness are not out of the question
• View From the Interior of a Warp Field
• As the ship within the field is encapsulated, so the ship is cut off from the outside universe. It is conceivable that the field may be permeable to light, but it also possible that the field may completely opaque. Depending on the field properties, crew within such a ship may see no change at warp, or else see nothing at all, depending on circumstances. Many scientists think a starship may then be blind as a bat, but as many think that you should see stars, albeit with optical effects such as dimming, and possible polarisation within the field. Flip a coin !
• The View at Warp
• As noted above, if the field is opaque, crew will not be able to 'see' anything, and will rely on sensors - such as gravitic sensors - to see outside of the Warp Field. The bridge would then present a computer projection of space outside of the ship, for navigational purposes.However, if the field is somewhat permeable to light, a number of interesting effects will be seen by the crewmember:- Blueshift and Redshift are relativistic phenomena. With an Alcubierre Warp Field, neither ship nor universe will be experiencing space-time contraction. While a ship in the normal universe will definitely experience blue- and red-shift opitcal effects, neither the ship in the bubble nor the outer universe will be dilated in time, and only in space. Relativity plays no part, and so stars 'outside' will not display any relativistic to occupants 'inside'. This is not to say that these phenomena, for an observer 'coasting' on the immediate outside of the shell moving at many times the speed of light, will not exist - it is merely that the light, on entering the warp bubble, will of necessity need to change its metrical frame - and in so doing, will revert to the values it would hold in a universe wherein the observer is at rest in respect to the photons within the frame of reference. This is based on the assumption that the ship within the bubble is at rest, and therefore not in motion, and further working on the assumption that the spacetime within the bubble is equally at rest. Light entering the bubble will need to adjust to this quantum state, and will most likely do so by exchanging the quantum state it had on entry with that of the bubble within which the ship is resting in.- From within, stars will appear to be static ahead, static behind, and drifting slowly past the ship as it passes them by. The rate of drift depends on the bubble's velocity. At velocities of between 2 and 5 lights (i.e. multiples of c, the speed of light), only nearby dwarf stars will appear to move relative to the ship. In speeds of between 20-50 lights, there will be marked stellar motion - close by stars will appear to shoot past, while more distant stars will appear more static, but at visual radii of 50 ly, will have a visually apprehendable motion. More distant stars will appear nearly static. As speeds approach a kilolight (1000x lightspeed), so the stars will appear to blur more and more. At speeds of 32 kilolights, it will take 4 years to travel across a galactic arm, and at 320 kilolights, it will be possible to get from Earth to the Galactic Core in a decade.
• Outside the Ship
• As a ship arcs away from an external viewer, it will either blink out of existence in an opaque field, or else turn away, and vanish in the distance. As it does so, it will appear to lengthen and distort at its nose, while it tail appears less distorted. As it dissapears from sight, the quantum boundary will begin to emit photons at progressively higher and higher energy bands, and the shell, on disappearance, will be a heavy emitter of Cherenkov radiations. Presumably, a ship designed for high efficiency will possess field manipulation technology that will permit to to limit these energy sapping radiations, though it is certainly possible for them to exist anyway.
• Hyper-drive - the Star Trek Warp Drive from 2009 onwardsin the new J.J. Abrams directed feature film, Star Trek (2009), the Warp Drive's characteristics are more in keeping with another staple of SF, the Hyperdrive. A Hyperdrive will catapult the ship into a part of space which is outside of normal space, permit trans-luminal flight, and then drop the ship back into normal space upon reaching its destination. At present, a Hyperdrive is a real possiblity, thanks to a real world physical phenomenon - Quantum tunnelling, where an atom will jump from one place to another without appearing to travel through the intervening distance. Its a statistical effect, and many atoms - for which read most - do not do it. But it does happen, and the fervent wish s that it will ultimately become controllable. When it does - humanity will build a hypership, presumably.
• View at Warp
• Assuming Zero-time jumps, there will be no view per-se: now your here, now you are there. But in travelling over interstellar distances, its entirely possible that a duration will become part of a voyage. Assuming this, the visual effect in the recent movie Star Trek is pretty spot on - at most, a Cherenkov aura of light will accompany motion through space as bleed through from not unnaturally slightly imperfect technology makes its way thought into the space-field - or sub-space, as Star Trek aficionados know it -into the ship's local environment.

Some other notes:

The View at Warp may be impossible to see, or even then require computer support to make the view comprehensible. It is implicitly stated in most hard SF like Star Trek, that the view outside the ship is computer generated, enhanced, and definitely jazzed up (the inclusion of sound, for instance) so that the human (and alien) pilots and crew of such a ship would then be able to more readily react to phenomena outside of the ship. the extreme distances in space require that visual shorthands like this allow for a more functional management of situations - the human eye , for instance, would not see stars, be blinded by distant suns and nearby planets, not be ale to detect ships at even 100km distance, nor discern friendly ships unless a few hundred meters off the port bow !