How do I set a conditional breakpoint in gdb, when char* x points to a string whose value equals "hello"?

You can use strcmp:

break x:20 if strcmp(y, "hello") == 0

20 is line number, x can be any filename and y can be any variable.

break x if ((int)strcmp(y, "hello")) == 0

On some implementations gdb might not know the return type of strcmp. That means you would have to cast, otherwise it would always evaluate to true!

Since GDB 7.5 you can use these native Convenience Functions:

$_memeq(buf1, buf2, length)
$_regex(str, regex)
$_streq(str1, str2)
$_strlen(str)

Seems quite less problematic than having to execute a "foreign" strcmp() on the process' stack each time the breakpoint is hit. This is especially true for debugging multithreaded processes.

Note your GDB needs to be compiled with Python support, which is not an issue with current linux distros. To be sure, you can check it by running show configuration inside GDB and searching for --with-python. This little oneliner does the trick, too:

$ gdb -n -quiet -batch -ex 'show configuration' | grep 'with-python'
             --with-python=/usr (relocatable)

For your demo case, the usage would be

break <where> if $_streq(x, "hello")

or, if your breakpoint already exists and you just want to add the condition to it

condition <breakpoint number> $_streq(x, "hello")

$_streq only matches the whole string, so if you want something more cunning you should use $_regex, which supports the Python regular expression syntax.