First of all, your people have to acknowledge that they are part of a team. You can reinforce this by holding team meetings, posting team news on the bulletin board or your intranet page, and tracking team performance against team goals.
Secondly, they have to believe that the team is capable of producing more than the sum of its members. Lance Armstrong is a great bicycle racer, but he could not have won the Tour de France without the support and assistance of his team members. You may have a great customer service rep on your team, but without the cooperation of the other members of the team he or she would not be able to handle as many calls. You have to make this readily apparent to them and clearly delineate the increased rewards they can achieve through teamwork.
Reinforce Team Building Efforts
One company I know had a great customer support team. Their director challenged the team with higher and higher goals. He celebrated their successes in meeting and exceeding those team goals. He also celebrated them as individuals. The team decorated the cubicle of everyone who was having a birthday. They did community service projects together. They had fun at work. And they enjoyed beating the goals Clint set for their team. They got a significant boost in self esteem from belonging to a winning team.
Making up t-shirts, etc. with a team logo or motto can help reinforce the sense of team identity, but it's not required. You should know your team well enough to know whether or not something like that would be positive reinforcement for them.
Don't make the mistake of one Accounting Manager I knew. The motto he picked for his team and had printed on ball caps he gave them didn't fly. He hadn't involved the team in selecting either the motto or the object on which it was printed.
I recommend you develop your own exercises where possible. No outside consulting company knows your company culture as well as you do. You can do a variety of exercises or play a variety of sports. I have built successful team building exercises around golf (for non golfers) and bowling. Another currently popular team building exercise is Paintball.