After googling for some time, I realize that it is due to lack of the library `libstdc++.so.5'. This is one of the old versions of C++ libraries, most of current Linux distributions do not install this library by default. The method to solve 'Downloading bookmarks' problem is:
1. Install the package that contains libstdc++.so.5. For Fedora 8:
# yum install compat-libstdc++-33
For other distributions, you should install the corresponding packages.
# sudo apt-get install libstdc++5
2. Exit Firefox, restart Firefox, re-install Google Toolbar. This is very important, or else the problem will not be solved!
3. Restart Firefox. Now you can see all your bookmarks in your Google toolbar!