Can someone advise me as to which website to use to purchase roundtrip train tickets from Cologne to Liege, and again one week later from Cologne to Brussels. We are a family of three, 2 adults and 1 18 year old. Should I buy a pass or purchase individual tickets? I have seen a great variation in prices and am unsure of the best deal. We also will take a day trip from Brussels to Brugge.

These are very inexpensive fares and thus you should just wait until getting to Cologne to buy these tickets - i don't think you'd save any money online.

That said the discrepancy you may be seeing in prices is perhaps because there are two types of trains running this route - the generally more expensive and reservations obligatory Thalys trains and the generally less expensive and non-requiring reservations German ICE trains - the latter you can make seat reservations on when buying your ticket but personally i wouldn't sweat it - based on my 1000s of such train trips. There is no reason for you to take the Thalys trains, which continue onto Paris via Brussels if you are terminating in Liege and Brussels. www.bahn.de for schedules and pricing in euros. (A handy way to reach the English schedule page of the Wunderbar German rail, bahn.de site is to go to: www.budgeteuropetravel.com on on their home page click on the link All European Railway Timetables or some such wording and up pops the English schedule page with two boxes where you put in Cologne and Liege, the date and all the schedules pop up with pricing details. Raileurope in US sells these tickets, but currently at highly inflated prices over what you'd pay in Cologne. And again there will be NO problem getting on the ICE trains IMExperience. Buy the Brussels-Bruges day return ticket in Brussels (and tell the clerk you going and coming back the same day - at times Day Returns can be much cheaper than two one-ways. You can get schedules for Brussels-Bruges on the bahn.de site but not pricing as it's not a German train, but the cost is negligible.

Again don't even think about any railpass!

There is no pass you should consider that i know of.

So kind of you to offer such a detailed response. The Bahn website quotes fares of about 21E per person, one-way for RE or ICE service. The Thalys Voyages quotes $36.50 E per person round trip. Am I missing something? At these rates, and since we are three, it may be cheaper to simply rent a car for a day and a half. We are arriving one day early in Cologne in hopes of seeing the Christmas market in Liege. We leave the next day for a flight to Munich.

A car will undoubtedly offer you motre flkexibility but consider the cost of insurance if any, the cost of fuel, the cost and availability of parking and the time it will take to pick up and drop the car not to mention the possible stress of driving in an unfamiliar area.

140 km each way Cologne to Brussels or about 75 miles.

You're not missing something. The fares you quote are normal prices. It's the border crossings that make your journeys expensive.
FYI Brussels - Brugge roundtrip costs 23.60 euro (pp) on weekdays / 12.60 euro on weekends.
Driving from Cologne to Liège isn't a big deal ; to Brussels (especially IN Brussels) might be a nightmare unless you travel during the weekend. Or you rent a car with GPS.
Furthermore everything has been said by PalenqueBob.

Thanks to all for kind responses. I didn't mean I would drive to Brussels, just to Liege as we are only going there for one night at the beginning of our trip to see the Christmas markets. Our trip to Brussels isn't until the following week. Are there any comments on the feasibility of driving to Liege for one night and then returning the car back to the Cologne airport?
I will definitely take the train from

I will definitely take the train the following week to and from Brussels and to Brugge on the weekend. Palenquebob's tips were very helpful for that trip.

Cologne-Liège is 130 km or one and a half hour drive. It's all motorway. There are roadworks going on between Cologne and Aachen on the A4 until Dec. 31st. Don't know how these will affect traffic.
For driving directions and a route map, check out www.viamichelin.com
For parking facilities in Liège, use the 'map' button on top of the www.viamichelin.com site, fill in 'Liège' in the destination box and check the box 'Car Parks' on the map.