does firewire still work?

A friend is purchasing a new iMac, and wants to transfer all the data from her old computer to the new one. I had recommended using firewire, but it
seems the new iMac may not have the connections for this. I'm told that it's necessary to buy a £35 Thunderbolt wire instead. Is this really necessary - and why?

Have to keep up with the times.

The first reason would be that there is no FW port on a new iMac.
It has USB 3 and Thunderbolt (TB) ports.
These are the current standards - the ones being mass produced.

See the following for importing to a new Mac that would be running OS X 10.9 Mavericks - link.

For only a one time transfer of the existing data to the new machine - I'd just use wifi or ethernet instead of buying an adapter/cable.

Or, if purchasing from an Apple store, take the existing machine in when buying the new one and they'll do the transfer for you.

If your friend is already using FW (has the cable) for their externals/backups, TB is compatible with FW and you'll need a TB to FW adapter (this is a FW800 connection).

Note:
While there are still some on the retailers shelves, WD has already quit producing FW externals and pretty sure the other drive manufacturers have also. OWC still has them and probably a few other specialty companies. I've been too cheap to move to TB. Since my Mac has USB 2 and TB - I am using the TB to FW for my external backups.

What ports are on your friends Mac? Don't be confused by mini display ports, they look the same but won't have the thunderbolt symbol adjacent to them. Realistic options are as bobtomay says, if you are buying from an Apple Store let Apple transfer for free, ethernet, the cheapest option for DIY, or if your friend has FW drives and wants to use them on the new Mac, then consider the thunderbolt to FW800 adapter, as it will get utilised later. I'm upgrading soon, and will be leaving my FW drives behind, as USB3 is so much faster and large drives are so much cheaper now, so if she has FW drives, she might want to reconsider retaining them.

Brilliant, thanks to both of you She'll use ethernet and Migrations.

For what its worth, I just looked at doing a migration from my old MBP to my new mid 2012 MBP (still has FW ports) and couldn't get Migration Assistant to see my old MBP when booted into Target Mode.
Not sure why, as I have used this method for 4 previous migrations, but I could see the old MBP on my desktop as an external HD, but Migration Assistant didn't see it.