I have never used a MAC but assuming it can use an FTP client program the same way that a windows pc can then you should be able to FTP the files across.
On windows I use Filezilla FTP client which is a free one and works well between linux boxes and windows pcs.
I just had a look on their site and they do a MAC version so it should work.
Just install and add your DMs LAN IP address and username and password into the settings and when you connect the computer shows in the left window and the DM in the right window. Go the the folder on your computer where you want to save the files to in the left window and go to the hard drive in the right window and drag the files across.
Thats all there is to it.
If you have any problems post again 
could always setup a samba fileshare on your dreambox too
Thanks for your suggestion, Sandra. I downloaded FileZilla and filled in the fields at the top of the screen as follows:
However, when I clicked the "Quickconnect" tab, FileZilla "could not connect to server". I got the same result using a Windows 7 laptop, so it is not due to using a Mac.
Could you please tell me what I did wrong? 
I think its probably because you have used the quick connect rather than set up the connection using the site manager first. Depending on which server type and logon you need to have something in front of the IP address when you do it that way.
Go to File and then open the Site Manager, click on My Sites in the left window then on New Site.
Put your IP address in host, port 80 although that doesnt seem to matter if using standard FTP, Server Type should be FTP- File Transfer Protocol and Logon Type change to Normal, default is anonymous. ( This being set to anonymous is almost certainly why its not working )
Put your user and password in and click connect and that should work fine this time.
I usually right click on the new site and rename it as whichever box I am setting up but if you only have the one box you can leave it as New Site.
Once the info is in there you can then use the quick connect boxes but you need to put ftp://your.box.lan.ip as the host, if using that method.
As I have a couple of boxes connected and sometimes do them for other people, I find it quicker to click on the drop down arrow just below File and that opens and shows me a selection of the names of the sites I have set up so I can just click on the name of the one I want and it connects.
Hope thats sorts it out OK, if not get back to me
I didnt pick up on the port number being incorrect. FTP uses port 21, port 80 is for HTTP.
Following Sandra's instuctions and using a laptop running Windows 7 to connect to the Dreambox, I input the following in the general settings of FileZilla's site manager:
Host: 192.168.1.34 (shown on the front pannel after connecting the DM to Residential Wireless ADSL2+ Gateway and turning it on while holding the channel down button down)
Port: (I left this blank, but even using 21 I got the same result)
Server Type: FTP
Logon type: Normal
User: root (the default, which I have never knowingly changed)
Password: dreambox (the default, as above. Not using any password did not change the result)
The response was:
Status: Connecting to 192.168.1.34:21...
Error: Connection timed out
Error: Could not connect to server
Status: Waiting to retry...
Status: Connecting to 192.168.1.34:21...
Error: Connection timed out
Error: Could not connect to server
The Communication setup window in the Dreambox's Expert Setup has the following data:
IP: 192.168.1.34 The DHCP box is not ticked.
Netmask: 255.255.255.0
Type: LAN (the only type shown in the drop-down list)
Nameserver: 192.168.1.1
Gateway: 192.168.1.1 (the address of the Residential Wireless ADSL2+ Gateway)
The enable Network box is ticked and the port box shows 21.
I checked whether the ethernet cable worked by using it with other equipment and there were no problems.
I would be grateful if anyone could tell me what to do. 
You said that the LAN IP of the dreambox was 10.0.0.7 yet today its 192.168.1.34
Did you connect an ethernet cable directly from your laptop to the DM, without using the router on monday as the 10 IP range is sometimes used by ad hoc networking but if you did that then you would need a crossed ethernet cable not a straight or patch cable.
Somethings changed since your last pm to me as you are now getting the IP address showing in the front panel so we are getting somewhere slowly but surely.
I think the problem has to be the user name and password not being correct.
I suggest you download DCC from this page and that should test your connection and show if your password and usernames are correct.
Thats great, we have it connecting now.
The Local site on the left is your computer, you can browse through the folders in the top part for quick access and that folder and its subfolders will show in the main left window. The Remote site on the right is your Dreambox.
In the right hand window, the lower one, you have all those folders that you listed.
Double click on the folder called HDD to open it, you will see a mesage at the top of the screen saying retrieving directory listing, this could take a few seconds to open.
Now in the folder you will see a few more subfolders and logfiles. One of the folders is called Movies. Double click on that to open it.
All your recordings are listed in there.
Each recording will have 4 files but the one you want is the largest file and will have the file extension .ts with nothing after it.
In the left hand window find the folder or make a new one, on your pc where you want to copy the film to and have that folder opened.
Then just drag the .ts file from the right window to the left one.
There is a small window at the bottom of filezilla which will show the transfer starting and its progress and how long it will take.
Once its transferred you can close filezilla or transfer another recording.
Hope that explains it all clearly enough but if you have any questions just ask again
I am afraid that has got me beat at the moment
I cant see any reason why it should time out before listing the contents of the movie folder and allowing you to transfer them to your pc.
Can anyone else think of why this is happening ?
Has nobody any ideas about why the connection is timing out when trying to open the movie folder
I am pleased that you managed to work out what the problem was at last, its handy to know for future reference
The only files you need to transfer to the laptop to play on it and to burn to DVD are the .ts ones. You dont need the EIT or EPL ones, they must be something to do with how the dreambox identifies and arranges them.
You should be able to play the .ts files on your laptop with most media players, I tend to use VLC as I like the interface.
If you have Nero then you can use Nero Vision to burn the .ts file or files to make a DVD that will play on a stand alone TV DVD player, other burning programs will also do it.
The reason you are getting the .ts + .ts.001 + .ts.002 files is that your dreambox is limiting the size to a maximum of 1gig. On my TM9100 there was an option to change the maximum recording size so that I could have a single .ts file for each film. My DM 8000 just records as a single .ts file. I dont know if you have the option on the DM 7020 to allow it to make bigger .ts files or not but if it does you could increase the limit so that you would have a single file to transfer, view and burn. If not it doesnt matter as Nero Vision will add the files together and make a DVD from them.
