I'm trying connect to MySQL 5.1 on Fedora 11 from an external computer and am having difficulty.
I'm quite certain that I've executed the correct GRANT commands.
The problem seems to be with the connection itself.
The firewall is configured to allow traffic to port 3306 but my attempts to connect are being denied.

C:\WINDOWS\system32>telnet 192.168.1.10 3306
Connecting To 192.168.1.10...Could not open connection to the host, on port 3306: Connect failed

I found this troubleshooting page:
MySQL :: MySQL 5.1 Reference Manual :: 5.4.7 Causes of Access-Denied Errors

It suggests that mysql might have been started with --skip-networking or --bind-address=127.0.0.1.

The bash scripts that come with fedora are a little hard for me to read but I didn't see them in there.
I looked in /etc/init.d/mysqld.
This shell script seemed to be invoking /usr/bin/mysqld_safe which also didn't have these options specified.
Nor did I find anything in /etc/my.cnt.

Anybody have any suggestions?

This article solved my problem:
How Do I Enable Remote Access To MySQL Database Server?

Needed to add this:
bind-address=YOUR-SERVER-IP
to the [mysqld] section of /etc/my.cnt