Someone else once mentioned that it was possible to visit the underground area and third level at specific times without a tour, but I've never seen it on an official site; however, the link I gave is for the Rome tourist office, which is usually reliable. If you want to do that, I suggest you call the number given. If you would report back to us, it would be very useful.
As Donna says, there are now reports of long lines sometimes at the Roman Forum and Palatine Hill entrances. The best time to try would be in the afternoon. I think the two museums I mentioned above would be your best opportunities of buying tickets at the last minutes, if you should happen to be near either one. As I said, they are both part of the National Roman Museum, which has four sites, and they're one of Rome's best bargains. The ticket is only 7 euros, and gives access to all four museums, over a period of three days. One of the four, Palazzo Massimo alle Terme is one of Rome's foremost museums, with a superb collection of ancient sculpture, as well as splendid mosaics and some fine wall frescoes from the villa of Livia, wife of the Emperor Augustus. This museum is very near Termini station, and is also near the Museum of the Diocletian Baths, another very interesting museum, which is one of the places where you can buy Colosseum tickets.