If you use a GFCI outlet and the rest of the outlets downstream don't have a ground wire attached, are they still considered grounded and are they safe?
No, they are not grounded.
Yes, they are GFCI protected (as long as they are on the LOAD side of the GFCI).
You are allowed to protect older ungrounded outlets by GFCI protecting them, though it's still preferable (but more invasive) to actually get ground wires everywhere. If you have any 3-prong outlets without a ground, they must be GFCI protected and labelled "No equipment ground".
Tester101 nailed the question, so I'll cover another option.
Depending on your situation, it is often possible to retrofit ground. Normally, wires in a circuit must be kept together for good reason. Ground is a special case, it can be routed separately from the other wires in a retrofit situation.
That is because ground is not used to flow current except in a fault condition (when a breaker is about to trip). The job of the ground is to give a nice easy path for the fault current to flow back to the service panel (breaker box) and trip the breaker, without passing through any humans or setting anything on fire.
Does a GFCI make an ungrounded circuit safe? The GFCI is comparing the current on "hot" and "neutral". If they are the same, all the current is accounted for, and none of it is shocking anyone. The issue is whether the GFCI is precise enough to detect a dangerous current - this varies. 10ma is enough to knock someone out, and that is fatal in some instances (they fall, they drown). The other issues relate to equipment: RF noise causing problems, etc. The equipment may not perform well without a true ground.
are they still considered grounded
and are they safe?
Safe is not a binary thing.
Code in the USA allows a number of things for retrofits that are not allowed in new work. It is difficult to force people to get work done and perfect can be the enemy of better. Whenever you see something that is allowed for retrofits but not for new installations you should be thinking "the code writers thought this was the lesser evil", not "the code writers thought this was perfectly fine".
In practice if people live in a house that only has 2 pin sockets that won't stop them from using appliances that need a ground. They will cut the pins off, or use cheater plugs or do something to make their appliances work.
The gold standard for grounding is ground wires that follow the current carrying wires. but ground wires that follow a path different from the current carrying wires are better than not having ground wires at all and GFCIs go some way to mitigate the risks of a missing ground.