I've been toying around with 360 reviews, and like them. From a tools perspective, there are probably many out there that do a great job. Unfortunately, it can take a great deal of time to investigate several solutions, especially if you need to contact the companies, or pay upfront without seeing the systems in action. I wasn't able to find one that I could easily try without signing up, so I created one.
Take a look at CircleStats. It facilitates the 360 review process and presents the results in a very visual way.
If not for your team, you should at least know if there's a discrepancy between how you think you're doing in an area, and how others think you're doing in that same area. If taken with a grain of salt, you can learn more about how you're doing from 360 review feedback than you can in talking to peers, direct reports, and managers, even if you talk often.