In slackware-13.0 dolphin (opened as a regular user) is not able to open partitions (fat, ntfs and ext4). It gives access denied message.

When I open dolphin as root with 'kdesu dolphin' command, the partitions apparently get mounted but are not displayed in dolphin window. There is an error message:
In this case partitions can be accessed in command line window of dolphin opened with F4 key.

How do I solve this. Thanks for your help.

By editing /etc/fstab. http://slackwiki.com/Fstab

But I don't want all partitions to be mounted at startup. I want to mount them through the file manager if I need them. Is it possible?

Yes.
Oh, you want a hint? Look at the 'users' option.

Thanks for this good link. I just want to clarify that to have partions mounted so that they are accessible to all users for read and write, following can be the entries:

for NTFS partition:
for FAT32 partition:
(above was used for slackware during installation)

What should be the line for ext4 partitions?

I want to install slackware on external hard disk and use it on different computers. Hence, I do not want to mount partitions from /etc/fstab file. I ubuntu, I have similar system. Once I open file manager nautilus as root, I can access all partitions that are available on the system, even though there is no entry in /etc/fstab file. In slackware, when I open dolphin after becoming root with 'su -' command or with command 'kdesu dolphin', all the partitions are listed on the left side but they cannot be accessed as I mentioned above. How do I overcome this problem. Thanks for your help.

In Slackware 13.0 there was a bug with this. Try

Thanks. It works perfectly. I had stopped using slackware because I was not able to access the partitions easily.