Doesn't look too bad, especially by Apple standards. A 1.25GHz Mac mini with the essential 512MB of memory, keyboard and mouse comes out at £427.01 ($804) at Apple Store UK. That is without a screen, of course, but includes free delivery.
For comparison, a 2.6GHz Dell Dimension 2400 (D01245) -- priced to sell at £330 as standard -- currently comes out at £447, including 512MB of memory, a Firewire port (£23.50 extra), a 17in CRT monitor, VAT and shipping.
The market may be a bit tougher in the US, where the bare Mini mac costs "from $499" (£265). You can get a 2.66GHz eMachines Desktop PC (T2862) from Circuit City for $449.99 (£239), or an even more attractive $299.99 (159.36) after rebates.
Update: Actually, the Mac mini looks to be at least half the price of a similar PC, if you really want something that small, and you are not planning to assemble it yourself. Small form factor PCs don't seem to have a very good survival rate -- even HP's ePC has vanished -- and the Jadetec, for example, costs £740 with a CD-ROM instead of a combo drive. (Tom's Hardware has some good pics here from 2002.) Otherwise, the novel Nanode won't be out until Q2 this year.
I bet the guys at Via are rubbing their hands at the prospect of selling their 12 x 12cm Nano-ITX motherboards to PC cloners who want to make Mac mini knock-offs.