Now that Elon Musk has released engineering targets for the proposed interplanetary transport system (formerly BFR), there is some meat to work with when looking at possible applications. I'm going to extrapolate, extend and abuse those numbers as thoroughly as I can after the jump.
First off, let's look at the booster. 275 tons of dry mass, return to launch pad recovery using 7% of the fuel load (which is 469 tons) and total propellant capacity of 6700 tons. The return fuel provides about 3.5km/s of dV, allowing for the boost-back, deceleration and landing burns. All of the dV numbers to follow assume sea-level Isp for the first stage engines, so this is a conservative value. In reality the craft spends most of its time out of the bulk of the atmosphere and Isp increases rapidly into the 370's during the ascent.
Elon mentioned that it can probably SSTO; that's true but you have to cut the landing propellant by quite a bit to make it happen. I think if the booster can survive orbital reentry then a lot of the boost-back burn is eliminated because you can simply wait in orbit until your path lines up with the launch site and let the atmosphere do most of the work. At any rate, assuming an Isp of 361 and reserving 200 tons of propellant for landing, the booster can SSTO 40 tons of payload with about 9.2km/s of dV. It would have to be something robust, or remember to subtract fairing mass from that number. Reusability after orbital re-entry for the booster is questionable, but if it works then this machine would put everyone else out of business.
A more normal mission profile is to carry either a lander or a tanker. That's 2400 tons (lander with 300t cargo) or 2590 tons (tanker with 380t fuel as payload); in this configuration the booster provides 3.8 to 4.0 km/s of dV to the upper stage. Actual separation velocity is 2.4 km/s, so drag and gravity losses are in the 1.4 to 1.6 km/s range. (Nearly all of these losses are spent by the first stage.)
A tanker launch is heavier, so stage 1 gives a bit less velocity (3732 m/s gross). The tanker itself has a little more juice available (6016m/s), so the stack still has about 9750m/s. The lander stack should be 3870m/s from the booster and 5625m/s from the lander, total of 9494m/s. The extra fuel in the tanker allows for orbital maneuvers. Both upper stages retain 1560-1580m/s worth of landing propellant, which is 50 tons for the tanker and 85 tons for the lander.
The booster is expected to cost about $230 million to fabricate and be reused for about a thousand launches. Maintenance runs about $200k per launch.
The tanker is a lightweight 90-ton fuel tank with engines and heatshield. Fully loaded it is 2590 tons and it can deliver 380 tons of fuel to a waiting lander in orbit. It returns to the surface and lands on legs; most of the dV for this is provided by aerodynamic drag on the heatshield. The tanker is expected to cost about $130 million to fabricate and be reused for about a hundred launches. Maintenance runs about $500k per launch.
The lander is a robust 150-ton interplanetary vehicle with 200 kW of solar panels. It can carry 300 tons to LEO. Once refueled it can carry up to 450 tons to the surface of Mars from LEO. The lander's abort to surface fuel plus five tanker trips will fully fuel the lander; Elon mentioned Mars trips with as few as three tanker trips, so not every launch window or cargo will require the full load of propellant. The pressurized volume has enough space for 100 passengers. The ship has a huge amount of extra delta-v available, so trips are expected to be as short as 90 days (90 to 150, average 115). The lander is expected to cost about $200 million to fabricate and be reused twelve times round-trip. (If it was used in LEO only then it would have reuse comparable to the tanker, around 100 flights.) Maintenance runs about $10 million per Mars flight, probably a tenth of that or less for LEO only.
In the reference plan, the lander is launched to LEO with passengers and cargo. The same booster launches a tanker three to five times; the tanker docks with the lander, transfers fuel, lands, reloads and repeats. Once the lander is ready to go it departs during the transfer window. Passengers cruise for about 115 days in microgravity using currently-available life support tech. The lander performs an aerocapture in Mars atmosphere with direct descent, flying sideways during the hot parts for maximum drag and then landing propulsively on the tail. ISRU equipment makes propellants for the return trip. When it is time to return, the lander launches from Mars surface to low orbit and shortly after departs for Earth. Earth arrival is just like Mars: aerocapture into direct descent. Passengers and cargo unload, then the ship gets a deep maintenance overhaul.
The first few flights carry a small ISRU plant as part of their cargo. This is enough to produce return fuel during one transfer window using the ship's solar array and probably some extra panels. Components would be an atmosphere compressor, ice excavators and water extraction oven for the raw materials, then electrolysis and Sabatier process equipment to make propellants, followed by liquefaction equipment to turn them into liquids. The very first flight will be unmanned and possibly the one after; passengers won't be sent until there is return propellant available. Later flights will rely on a built-up ISRU facility for refueling, freeing up some cargo capacity.
Musk expects the cost for these flights to eventually drop below $140k per ton of payload to Mars surface. If components don't meet their re-use targets the cost would go up, but even if the lander only gets used twice the price is still around $300k per ton. None of this includes the ~$10 billion estimated development costs. Consider that he had Raptor engine test firing video and pictures of a 12-meter carbon fiber propellant tank ready for the IAC this year, plus they've been doing simulations and refinements for about a decade; this is going to happen and it's going to happen soon. The only data they don't have in enough resolution is Mars EDL for larger objects with supersonic retropropulsion and a map of accessible water ice; the upcoming Red Dragon missions will help fill in the gaps.
Going beyond the plan
Elon mentioned several interesting destinations throughout the solar system, up to and including Kuiper belt objects provided there are propellant depots available. The easiest targets would be those with atmosphere for aerocapture, and anything with possible ISRU would be a good target as well. Targets beyond the main belt will likely require nuclear power of some kind.
A lander with no payload and ~85 tons of landing fuel has about 8.2km/s in the tank. The landing reserve is about 1.5km/s, so if you run the tanks dry you can get about 9.9 km/s. That's enough to go from Earth to nearly any main belt object (Ceres, Pallas, etc.) and make orbit. Payload to Ceres orbit would be 19 tons, for example, or 5 tons to Ceres surface. If you launch from Mars orbit fully fueled then you can just barely orbit Pluto on a Hohmann transfer (~46 years travel time), or you could take 70 tons to the surface of Vesta and back.
The tanker is a better option for deep space. It's lighter and carries more fuel, so in an expendable configuration it has about 12.5km/s available. At $130 million that's pretty affordable for a deep-space probe bus, especially a chemical one with over 12km/s dV.
I'm working on getting a trajectory optimization tool running with current data, so I haven't had a chance to find reasonable dV numbers for missions to Titan or other gas giant moons. It would be a pretty wild ride to aerocapture through Saturn or Jupiter and land on one of the moons, but if the mission is launched from Mars orbit you could put down quite a bit of payload. Hoping to have more numbers to work with soon.