When the GFCI outlets lose power, some of my "normal" outlets go out also. When I reset the GFCIs, these "normal" outlets return to power also. Are these "normal" outlets considered grounded?
The "normal" outlets that lose power have been wired to the LOAD terminals (i.e. downstream) of the GFCI -- if they are in a location that requires GFCI protection, this is normal to find.
They are considered equivalent to grounded outlets for shock protection purposes as well; however, without knowing how they are actually wired, we do not know if they are actually grounded or not.
Ground fault protection ensures that the current returning through your neutral line equals the current being drawn through your hot line, it does not necessarily mean that a grounding line is present. This protection is not the same as grounding, but is similar. Grounding primarily protects you against the short circuiting of a device that has a 3 prong cable. It's mostly limited to the short circuiting of the device itself because the grounding wire has to be attached to the conducting material that's causing the short, whereas a GFCI protects you against almost all short circuiting (except a short-circuit to neutral as Tester101 points out, but that should be handled by over-current protection). This is why GFCIs are required in bathrooms and kitchens where water can act as an ungrounded conductor. Although it offers broader protection, theoretically, a GFCI is slightly slower than grounding protection (but still fast enough to provide shock protection), so it's a good idea to have both for redundancy.
Normal non-GFCI outlets wired downstream in series with a GFCI outlet will be protected by that outlet's GFCI action. In fact, you can buy GFCI circuit breakers that provide protection to an entire circuit.
So in conclusion, your "normal" outlets may or may not have grounding protection, but the GFCI is providing the same effective protection. That being said, the more protection the better so I'd still check for grounding protection with a little gadget like this. If they aren't grounded, I'd be nervous about their age and/or the workmanship.