TV/VCR
110VAC, 50Hz. They will run if you connect them through a 220/110v transformer (you need to buy that here, not in the US - you can get one there - but they're expensive and they *are* frequency sensitive - a US transformer will run hot in Europe.
The TV system in the US is NTSC, most transmissions in Europe are PAL so your US systems won't pick up local TV (unless you're within range of an AFN transmitter, which would get you one or 2 channels.) Your US VCR will not record any PAL transmissions; the main use of the US TV/VCR would be to play any pre-recorded tapes you bring overr with you.
Your DVD player (Region 1) will work - it may be 110v only (in which case, you'll need the txfmr) or it may work on a range of AC voltages - check the manual. It will be useful for your collection of Region 1 DVDs, but almost certainly won't play European discs (few US models are multi-region.) NB - the output from your US DVD will probably be NTSC.
The solution is to either (a) bring the US TV *and* buy a PAL TV or (

to buy a multi-standard TV (receives most transmissions, works on 80-300 Volts AC.) Multi-Standard sets cost more than single standard and are not readily available in the US. It's almost certainly cheaper to bring your US DVD player and buy a European player (if you are going to rent European DVDs.)
PC - generally no problem. Check the back of the power supply - there should be a 110/220 switch. Most monitors accept either 110 or 220 volts without needing to change selection ... they're usually not marked with the supply voltage - but I haven't managed to blow one up in the last 12 years (and all of mine were purchased in the US.)
Printer and Fax Copier - usually detect power supply automatically. Shouldn't be a problem (but check the manual)
Other problems:
US Dishwashers - don't bring one. It probably won't work in Europe.
Washing machines/Dryers:
*Can* be adapted - the washer needs a 50Hz timer, the dryer needs some rewiring. Both need an on-board transformer (attaches to the frame inside.) The transformer should have a 100 volt (not 110 volt) output.
US Fridge/Freezers: need an onboard transformer with a 100v output. Any appliance with a large motor should be run from 100v rather than 110 because the motors will tend to run hot and will run slower. - You won't notice the reduced speed, but the increased heat output will reduce the life of the motor (the reduction to 100v will offset that.)
Think carefully before you bring large US appliances. Spare parts are not usually a problem, but fitting a large US appliance in a small European kitchen can be <img src="../images/emoticons/ytongue.gif">
Small appliances (hairdryers, coffee pots, toasters, blenders, Telephone answering machines, microwaves etc<img src="../images/emoticons/ysmile.gif">
Microwaves: Buy one here! Most US microwaves are dangerous if used on 50Hz supplies - they will run, but the magnetron will overheat. (There *are* some models which can be adjusted and some which adjust automatically, but they're not very common in the US.)
Other small kitchen appliances work (through a transformer) but items with timers such as coffee pots won't work properly, because the timer in US devices senses the mains frequency. We still have 60 seconds in a minute and 60 minutes in an hour, but your coffee pot will decide there are only 50 in each ...
Similarly, the date stamp on your US answering machine will be useless; your US phone will work here though you will need an adaptor from the RJ11 socket to whichever kind of phone socket you have - they're readily available.
If you have a hairdryer and it is 110v it will work in Europe, but don't plug it into the 110v shaver socket in the bathroom ... <img src="../images/emoticons/ywink.gif"> - you will need to use a transformer.
Transformers are a pain in the butt. I went from having transformers everywhere (long trailing cables to trip over) to re-wiring the house for 110 with US outlets - looks neat, but is a lot of work when you move out (and you ca nonly do that in your own place) to using European appliances where possible.
I have a US washer, Dryer and Fridge/Freezer - but they are 'loaners' provided by my wife's uncle and they run on 220v.