There's a Gantt View option for lists, I've tried that before and it's not bad, but I had problems when the project timeline was larger than the web part view, scrolling looked ugly. I'm sure some CSS could have fixed it up, but I wasn't looking to invest a lot of time in it, just experimenting. Definitely not comparable to MS Project or Project Server. I also tried putting a Ishikawa (fishbone) diagram web part I downloaded into a site, but it was nothing like what my PMO was expecting.
Ultimately, our PMO decided to make a custom project status slide in PowerPoint, including a Gantt Chart, risks, stakeholders, etc. They publish a separate one for each project weekly. I have them save the slide as a PDF document to their respective project library, name it the same thing each time (overwriting existing), then a custom home page for the site template looks for that document in the site's Shared Documents library and displays it in an iframe. The result is each project site's homepage has a Gantt Chart, risks, requirements, stakeholders, etc. in one shot. Works for us. Hope this helps!