Hello,
I've a 64-bit Ubuntu Linux machine.

Linux version 2.6.28-14-generic (buildd@yellow) (gcc version 4.3.3 (Ubuntu 4.3.3-5ubuntu4) ) #47-Ubuntu SMP Sat Jul 25 01:19:55 UTC 2009
Ubuntu 9.04 \n \l
Linux Debian 5.0 ( 2.6.28-14-generic x86_64)

When I tried to install the python-dev package on it using the
command
sudo apt-get install python-dev, I got following messages.

Reading package lists... Done
Building dependency tree
Reading state information... Done
The following NEW packages will be installed:
python-dev
0 upgraded, 1 newly installed, 0 to remove and 271 not upgraded.
Need to get 978B of archives.
After this operation, 24.6kB of additional disk space will be used.
WARNING: The following packages cannot be authenticated!
python-dev
Install these packages without verification [y/N]? y
Err http://in.archive.ubuntu.com jaunty/main python-dev 2.6.2-0ubuntu1
404 Not Found [IP: 91.189.88.45 80]
Failed to fetch http://in.archive.ubuntu.com/ubuntu/...buntu1_all.deb 404 Not Found [IP: 91.189.88.45 80]
E: Unable to fetch some archives, maybe run apt-get update or try with --fix-missing?

Tried with --fix-missing option as well. Same errors in this
case also.
Could someone please suggest how I can install python-dev
package on 64-bit Ubuntu Linux machine ?

Thank you,
Mahendra

404 error means its just not there, perhaps you need to add another repository:

Command line:
/etc/apt/sources.list

Synaptic:
https://help.ubuntu.com/community/Repositories/Ubuntu

Also there are two amd64 .debs for Ubuntu 9.04 python-dev here

https://launchpad.net/ubuntu/jaunty/+package/python-dev

Hope that helps.

Ubuntu 9.04 is End Of Life and no longer supported. I strongly recommend to use a recent version. You will get no security updates and bugfixes for this version, you will also have problems to install new software.
I would recommend to install 10.04 LTS, this version gets far longer support.