1. Basilica di San Pietro – St Peters Basilica
2. Cappella Sistina - Sistine Chapel (2 and 3 are in the Vatican city)
3. Colosseum
4. The Pantheon - I also saw a documentary on it last year and would agree.
5. Fontana di Trevi (Trevi Fountain)
6. Piazza di Spagna / the Spanish Steps
Copied the above from Niceoneted but placed in a different order. The Vatican including St Peters Bacicila and the Sistine Chapel are an absolute must see. Try to give this area a full day. Do the guided tour of the Vatican then re-trace your steps, there is an incredible amount to take in.
The Colosseum is amazing, again do the guided tour otherwise as with the Vatican it is difficult to really understand everything you are seeing. About 2 hours in total.
The queues can seem long but they actually fly along.
Trevi Fountain itself is stunning but surrounded by buildings, kind of looks like it was dropped into the wrong place. Spanish steps are worth seeing and are close to the Trevi but a bit over rated in my opinion.
Campo de Flori (sp) is a lovely little square surrounded with restaurants and there are also lots near the Spanish steps, food is really good in both areas and not expensive.
Comfortable shoes as already stated are a must. The Italians are really friendly and helpful and fabulous looking. Don't blame your wife if her eyes stray a little
The hotel we stayed in had tourist maps which were really useful. All the main places listed above are in quite a compact area so can be walked to or a short taxi hop away.
If I remember correctly the taxi fare from the Airport was €40 between two.
Have a great trip, I hope to return myself next year. LS.