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If you really, really, don't care about getting from one place in space to another quickly, a solar sail can be a good option. A solar sail is light (no pun intended) and requires no onboard fuel. At first glance, it sounds like an aerospace engineer's dream. The big issue, though, is that it takes a long time to accelerate to meaningful speeds. The problem can be tamed a little by making the solar sail bigger, but that means that it can become unwieldy (and thus harder to deploy), and a little hard to stuff into a rocket. So once again, here I go with a "size" question:

How big can solar sails reasonably become (assuming finite resources)? What are the biggest ones currently on the drawing board?

Finally, as called2voyage has pointed out, you could make a very large solar sail with "an asteroid and a 3-D printer." Is space-based manufacturing a reasonable option?

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    $\begingroup$ What if I told you that you didn't have to stuff it in a rocket? Give me an asteroid and a 3-D printer and I'll make you as big a sail as resources and structural engineering will allow. $\endgroup$ – called2voyage Sep 25 '14 at 21:01
  • $\begingroup$ @called2voyage Haha. I figured someone was going to bring up space-based manufacturing, although perhaps using different methods. I'll edit the question to see if I can cut that loophole. $\endgroup$ – HDE 226868 Sep 25 '14 at 22:36
  • $\begingroup$ Space-based manufacturing isn't a reasonable option... yet. $\endgroup$ – kim holder wants Monica back Sep 26 '14 at 0:37
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    $\begingroup$ @briligg You're referring to conclusions in recently published National Research Council study? Because it's been widely criticised for lack of vision and suggesting even more boards, panels, forums and alike should be established to "support" NASA endeavors in space-based additive manufacturing. They seem to prefer NASA would only 3D print more red tape in space. And we all know that red tape doesn't make for a particularly good solar sail. One does not reach space by anchoring in Washington. $\endgroup$ – TildalWave Sep 26 '14 at 8:23
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    $\begingroup$ While I don't know the limits I can see there would be limits. The bigger your sail the longer the cords that connect the sail to your spacecraft must be. Those cords have weight. Thus the bigger your sail the lower the ratio of sail area to total weight. $\endgroup$ – Loren Pechtel Sep 26 '14 at 21:14
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This is not a complete answer (there really isn't one, since what's considered "reasonable" will vary with the person answering), but:

With current technology, assuming that we didn't do fabrication in space (which would allow much thinner sails that don't require folding and packing in a rocket), and without relying on anything that hasn't been developed yet, solar sails can be made of 2 µm thick Mylar, which has a density of 1.39 g/cc, not counting the extremely thin layer of aluminum deposited onto it. This works out to approximately 360 m^2 per kilogram. Assuming the heaviest-lift booster for 2015 will be a Falcon Heavy (53,000 kg to LEO), that works out to 19 km^2, or if you prefer, a circular solar sail about 4.9 kilometers in diameter.

Note that this doesn't include the weight of the rigging, control systems, and so on that would be required, I just wanted to give a rough guide.

The best bet for a near-future solar sail really would be space-based manufacturing, though. Per Wikipedia, an engineer named Eric Drexler has created 0.1 µm aluminum film using vapor deposition. Space-based manufacturing (presumably using an asteroid as feedstock) would allow arbitrarily large solar-sails to be constructed.

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