Candidates have gotten so used to positioning themselves as good 'team' players that oftentimes, during an interview, they forget to include the all-important word 'I'. "...so, tell me about your most recent project and describe for me some of the obstacles. What was the scope, what were the deliverables and what was the actual vs. anticipated outcome?" Questions like these are clearly geared toward learning about YOU and while it's important to convey that you're an excellent team player, you shouldn't shy away from describing your individual contribution(s).
"Interesting question Ms/Mr hiring authority. When I was with ABC company we faced a similar set of challenges/milestones/obstacles and the team and I collaborated in such a way that I was able to implement/sell/transform/deliver..." or something along those lines.
From my chair this answer sounds way better than blurting, "I'm a solid individual contributor and an excellent team player where we worked on blah, blah, blah and were responsible and/or recognized as a team for blah...." Absolutely nothing wrong with describing team performance as long as you include the specifics of what you did so as to convey a sense of your impact/contributions. To further demonstrate the importance of focusing on the 'I' as a good team player, I'll borrow the words of flight attendants during pre-flight when they suggest to, "first put the oxygen mask on yourself and then help those around you". Years ago I was asked to define a good team player and I still maintain that what I believed then is true today and that the best team player is usually the strongest individual contributor(s) willing to work with other people toward a common objective. Respectfully, if you aren't good at what you do and can't deliver results for yourself, how can you expect or be expected to deliver more than that for the team...any team?
Just a reminder as I wrap up this post; the interview is YOUR opportunity to sell yourself, so go ahead and ring your own bell a bit. Obviously the goal here is to offer the interviewer reasons to hire YOU, not the team, so definitely share your accomplishments in a confident manner leaving your ego at the door. Confidence is an asset, arrogance is usually deemed a liability, so confidently include what you did, the impact it had on the team/project/company, why it was significant, and what you learned from it that makes you an added value to future teams.
In closing, I was consulting with a hiring manager who was reviewing his interview notes on a candidate he'd recently interviewed but, when I asked him for his final assessment, he seemed uncertain. I probed to see if I could figure out what his hesitation was and wound up with this pearl, "...after an hour I still don't quite understand what this person's involvement was on any of their most recent projects even though they were all delivered successfully, on time and under budget." What I did understand involved a whole lot of we, us, and the team, which leaves me to wonder whether they're a good team player or just a player on a good team. I don't have a spot on my team for the latter"...vinny