Should I pre-arrange transport between airports and hotels?

I guess the question is, can you handle your luggage on public transportation? And, are you flying into these cities or taking trains? Or are you asking about buying long distance train/plane tickets in advance? Three questions.

I would probably take a taxi if they are available. Are the taxis safe and available? Will I get ripped off?

I am flying into various airports and need to take myself and my luggage to the hotels.

I'm not keen on spending money when I don't have to. Airports are usually very far out but still well connected to many places surrounding it. It honestly depends though! But if there's an option to take the bus I would personally take that. Plus, I arrive later at my destination that I planned 7/10 times. From my point of view, it makes no sense to pre-arrange transport since your driver might have to wait for hours for you! There are plenty of taxis at airports, you can use those.

I don't know a single airport that is not flooded with taxis. The normal caution is to take a taxi only from a taxi starter and verify the fare before getting in. Just how much luggage do you intend to have???

In my experience Taxis and taxi stands are the easiest things to find in European airports. Just look for a sign and go there. I have started taking taxis a lot and love it. It does cost more, but if that is a concern try to share a taxi with travel partner of others waiting for a taxi.

No need toptebookin Rome. The Official Rome taxis have a flat rate of €48 from the Airport (FCO) to a hotel within the traditional city walls. I believe that includes luggage but you should check. Make sure you are in the queue for the official taxis, and do not go with anyone who approaches you and offers a better rate.

Pre-arranging could pose a problem when you are delayed...as with flying landing times are never truly as expected. Airports are usually flooded with taxis. It is for you to be careful, verify the taxi is legit and try not to travel with too much luggage especially since you will be traveling alone.

No need to book ahead in Paris either. It's a flat fee from the airport to either Right Bank hotels (50 E) or Left Bank hotels (55 E).

Do heed what Frank says and don't pay any attention to the guys who come up to you in the airport and ask if you want a taxi. Go directly to the taxi stand line and let the manager at the curb point you to a taxi.

I did pre-book in Rome but was traveling with 5 and wanted a tour as well.

All of these airports have easy bus or train options into the cities but not necessarily to the door of your hotel. Paris and Rome have fixed rates for the taxi fares. Prague is one city with a reputation for duplicitous taxi drivers (make sure they use the meter) but the AE Airport Express bus worked great for me. A guidebook will advise you of the options for each city, or the airport web sites will, as well.

From Geneva to Annecy, for instance, this is the info from p. 770 of Rick Steves' France:

Arrival By Plane: From Geneva’s airport (GVA, www.gva.ch), Annecy is a 45-minute autoroute drive (Swiss vignette required; see page 766). To get from the airport to Annecy sans car, take the direct bus (6/day Mon-Sat, 2/day Sun, www.gva.ch), book a shuttle van in advance (www.genevashuttle.com), or make the cheap but scenic 2.5-hour slog by bus and train (10/day). Taxis charge an outrageous 200 Swiss francs. From Lyon’s St-Exupéry airport (LYS, www.lyonaeroports.com), allow 1.5 hours by car--all autoroute--or 2.5 hours by train (10/day). Geneva’s airport has a helpful transportation desk at baggage claim.

Check each city to verify if there are flat rates to train or airports
Most cities have them.
Print out your address including the Postal Code so there won't be any confusion.
Remember that legitimate taxi drivers always remain in their vehicle.

I was just in Amsterdam and found using the Airport Express bus 197 for 5 euro to be quite cheap and efficient, easy to catch right in front at Schiphol. I had a rolling suitcase and carry-on tote and had no problem at all. Check them out online and see if your hotel is near a stop--I was 2 blocks from the Rijksmuseum stop.

Prague I took a taxi, there's a counter and they ensure you get an official one and address is confirmed. It was fairly cheap, about a 25 minute ride.

Paris I took a taxi from the official stand, 55 euro to the Left bank.

If I deem public transport easy then I will always opt for that, but sometimes it's just better to take a taxi or research a shuttle--though I do like to just get to my hotel quickly.