The Roman Forum, along with the Colosseum, is a must-see. There are two entrances: one closer to the Palatine Hill (on Via di San Gregorio) and the other closer to the northwest end of the forum (on Via dei Fori Imperiali). If you go through the Palatine entrance, be warned that there is a hike to get to the forum. Don't bother with the audio guide. Even though they give you a labeled map of all the ruins, it is very hard to figure out what you are actually looking at (as the ruins themselves are not labeled). My traveling partner and I spent a long time trying to figure out what we were supposed to be looking at. I would highly recommend getting a guided tour or at least having a very good map. Highlights include the Tempio di Vesta, the Arco di Tito, the gigantic Basilica di Massenzio, and the Arco di Settimio Severo. The whole place is very interesting and layered with history, but don't expect to see complete structures. Most everything is a fragment (or single column) of what it once was. Overall, it took us about 3 hours to get through but probably would have been shorter if we had known what things were. Entrance to the Roman Forum is included with your ticket to the Colosseum (and also includes Palatine Hill, which you can access from the Roman Forum), so take advantage of it.
This review is the subjective opinion of a TripAdvisor member and not of TripAdvisor LLC.