In this thread, Panda mentioned the Heathrow Connect service. Thanks, Panda -- I had not heard about this option.

Are those trains similar to the Express trains in terms of available space for luggage, or are they more similar to the underground trains.

The cost differential is pretty substantial,(6.90 GBP as opposed to 15.50 GBP for the Express) and the difference in travel time is only about 10 minutes (plus the potential longer waiting time), so I'm thinking I may use this service at the end of February, unless someone tells me I will probably have to stand up in a crowded car.

Judy

There is not much differerence between Heathrow Connect and Express in terms of space, crowding etc.
Main differenece is that the Connect is a stopping train and is used a lot by airport workers.

Connect currently terminates at Central for Terminals 1,2,3, whilst the Express goes onto Terminal 4. (The Heathrow Express is free between Central and T4)
The other main difference is frequency, the Express runs daily every 15 minutes, Connect runs every 30, every 60 minutes on Sundays)

At the end of March all the above will change when Terminal 5 opens.

Judy, we took the Connect the other day. You follow the signs from the terminal, walk along a long hallway, and then get tickets from machines. The trains are clearly labeled "Express" or "Connect" so there's little confusion. Each car has just a few racks for luggage. We landed at 6:30 am, and as the Connect begins at Heathrow, there were hardly any people on the train. The trip took under 1/2 hour to Paddington.

Just another thought. There is also another very cheap unpublicised transfer from Heathrow run by National Express coaches.
They charge just 4 GBP (the same as the London Underground) between Heathrow and London Victoria, much more convenient for many hotels than Paddington.
The coaches are comfortable long distance coaches with toilets etc.

Big H is right about the cheap National Express bus alternative (lots of Expresses, aren't there?!) I didn't mention it in the thread in reply to Brenda as they are very limited in the late evening/night and then take about 45 mins in light traffic to get into Gloucester Road Bus Station or onto Victoria. They are the end of the trip for long distance coach travel from all over the UK and whether or not you and your luggage can get on depends on how many are getting off at Heathrow.

I was very grateful to them as a student and until recently was my mother's preferred method of choice for visiting us from the country. The drivers are usually friendly and helpful.

It is a much cheaper alternative than the train, but less of a walk up and get on frequent service than the same-priced tube. The coach does have the advantage that as everyone disembarks, you are not under so much pressure to look out for the right station to get off.

Choice, choices.