By now, everyone is certainly aware of the problems found on Endeavour's insulation tiles, caused by fragments of ice hitting the shuttle during launch. The impact cut a gouge in some insulation tiles, and NASA is still deciding what, if anything, to do about it. The astronauts do have materials to fix the insulation, if necessary, but that is a complicated manoeuvre because, well, the tiles are underneath the shuttle. Damaris Sarria, an astronaut-in-training and Thermal Protection Specialist, discusses the possible solutions in her blog, and NASA has a 3D video of the damaged area.
The impact site was photographed from the ISS before the shuttle coupled to it; since the Columbia accident (caused exactly by fragments of, in that case, foam hitting the underside of the orbiter), it is part of the standard procedure to position the shuttle "upside-down" so that it can be seen from the ISS (I don't know what will be done in the Hubble repair mission, though).
I thought this would be a good time to talk a little about the reason why the shuttle keeps being hit by debris during launch. At launch, the shuttle is attached to three other large structures: two solid-fuel rocket boosters, one on each side, and the large, orange fuel tank that is the source of all the problems.
The boosters provide most of the thrust to take the orbiter up, and are solely responsible for holding the weight of the fuel tank and the orbiter while still on the launch pad. On launch, 71% of the total thrust is provided by these rockets, and 100% of the smoke you see coming out of the shuttle when it's already on flight comes from them (most of the "smoke" around the launch pad is actually from the water being used to cool the platform). A failure in one of the boosters is what brought down Challenger, in 1986; a leak ruptured the external tank and caused it to blow up.
The orange external tank carries the fuel for the shuttle's main engines; these engines don't provide much of the power needed for lift-off, but they are what takes the shuttle into orbit, accelerating it from 5,000 to over 27,000 km/h after the boosters separate. The tank is the only part of the shuttle that's not reused; after the engines are turned off, the tank is discarded and falls into the sea (the boosters also fall into the sea, but they have parachutes and are recovered). The landing of the shuttle is mostly unpowered, with aerodynamic braking being used to reduce the speed of the orbiter.
The fuel inside the external tank is liquid oxygen and liquid hydrogen (which burn into water, thus no smoke from it), and herein lies the problem. Liquid hydrogen needs to be cooled down to -252.8 degrees Celsius (just over 20 kelvin), which means that the tank needs to be very well insulated. Because of that, it is covered with a 2.5-centimetre thick coating of polyisocyanurate foam (which also protects the tank for aerodynamic heating during launch).
And this is the foam that falls off during launch. Also, as it is not a perfect insulation, sometimes ice forms on the tank (especially if it's a humid day and the shuttle has been fuelled for a while before it's launched), and ice fragments can also fall off. The foam can't be more securely attached to the tank without increasing weight and cost significantly (it's worth noting that, in the first few launches of the shuttle, the tank was painted white; that alone adds almost 500kg to the launch weight, and that's why it's not done anymore), so there's no easy solution to the problem.
The routine of inspecting the shuttle from the ISS seems to be the best procedure to deal with the problem of damage to tiles from falling debris, especially considering that the shuttle is not going to be used for much longer; it's indeed best that NASA spend its money and energy in the next generation of vehicles, rather than trying to re-engineer the aging shuttles. Still, that will make every launch and landing very tense for all involved, including interested amateurs like me and you.