How do you book tickets in advance for Villa Borghese, Coliseum etc. without being hit by huge online booking charges?
Marie's right, but you do have a couple of alternative options.
Borghese requires reservations and there's no way around it. The closest I got was having my hotel call to make the reservation and they were kind enough to not pass the fee onto me. Even if you use the Roma Pass (more about that in a minute) you have to reserve with the Borghese and pay the reservation fee separately. If you do decide to use the Roma Pass, you cannot book the Borghese online. You will have to call or have your hotel call for you.
For the Colosseum, it's not actually necessary to prebook a reservation. The long lines are generally caused by ticket sales. The way around this is to either buy your ticket at another site (Palentine Hill or Roman Forum) that is on the same ticket as the Colosseum, or to use the Roma Pass.
The Roma Pass covers a number of sites in Rome and gives you the first two entries free and a small discount on any additional sites, PLUS a 3 day metro/bus pass. You can read more about it here: http://www.roninrome.com/2009/04/27/should-i-buy-a-roma-pass/ Whether or not it is more cost-effective to buy the Roma Pass depends on a number of factors.
The Vatican is the other site you may want reservations and it is NOT covered by the Roma Pass. I believe the reservation fee directly from the Vatican Museum is reasonable (2 euro I think). Alternatively, especially if you are traveling during the off-season, you may not need reservations for the Vatican if you time your visit well. Generally, afternoons are better than mornings, and you want to avoid the free Sundays at all costs.
Another way to reduce the fees you pay is to be sure to book directly with the site and not through a third party. You can also choose to look at the reservation fee as a small price to pay for the precious commodity that is your vacation time, which you'd otherwise spend waiting in line. :-)
Unfortunately they will all hit you with booking charges. But these are the official sites:
http://www.galleriaborghese.it/info-en.htm
http://www.pierreci.it/it/musei-e-monumenti/colosseo/prevendita-colosseo-singoli.aspx