If you were not thinking too much about power efficiency, a low-cost possibility would be to use an internally current-limited wall wart type transformer and a shunt regulator.
The regulator could be three cheap components, but would dissipate some power (get hot).
Its voltage could be set to clip ripple peaks to 4.20 or whatever and forget the capacitor.
But really, IMHO there is no sensible point in making a Liion charger without electronic regulation.
And if you are going to have any silicon in it at all, you might as well have a proper regulator.
Take a look at the amazing chips from Power Integrations for example.
The LinkSwitch-TN at
www.powerint.com can do the whole mains to battery thing without a transformer (providing you can't touch the battery during charging, this is OK. I wouldn't let a kid use it).
You would have to mess with the basic circuit a little to get the voltage precision up to the level required for Liion charging, but I suggest this is the way cheap chargers are likely to go - after all, the 12V car phone adapters you buy are not just a big resistor, which they could be, they are switching designs - and that must have proved to be the most cost-effective solution.
For example, the High-Side Buck – Optocoupler Feedback design with a precision 4.20V voltage sensor (The Nat Semi LM3620 would do - and it has 4.1 and 4.2V select pins).
An isolated design (where you can touch the battery during charging) would only be slightly more complicated.
I apologise if my concentration on regulation is hijacking the spirit of this posting, but I worry about explosions and fire in Liion charging and I am not sure there is an unregulated transformer-and-rectifier design that will provide a reasonable charge time combined with safe charging under all circumstances.
I will cease to hijack now!
Steve