Great skater and play-maker. He was also fairly responsible defensively on teams that weren't exactly the best when it came to defense (The early-to-mid 1980s North Stars).
Obviously, the knock on him was his size at 5'9" and 170 lbs but he played much larger than that. I never recall his size being much of a detriment to his playing style though. He was also one of those guys who almost always seemed to elevate his game in the postseason, too.
As others have already mentioned, his career was filled with peaks and valleys. Part of this was the product of injuries and playing on some poor teams, but it was also the result of having to reinvent his game so he could stay in the league for over 16 seasons.
His first full five seasons in the league were tremendous from an offensive standpoint (okay, 1984-85 was a letdown but the North Stars as a whole had an off year then). A nagging shoulder injury really threw his career off the rails from 1986-1988, but he returned to form from 1988-1991 where he may not have been the offensive force he once was, but his two-way game was excellent. In his last two years in Minnesota, it looked like his career was winding down as his offensive game appeared to have completely deserted him. With that said, he was one of their most reliable defensive players in 1992-93 after a fairly disappointing 1991-92 campaign.
He was not happy about leaving Minnesota for Dallas, but his first year in Texas was his best statistical season since 1990-91. The Stars declined in their sophomore season in Dallas and so did Broten until he was dealt to the New Jersey Devils. In New Jersey, Broten experienced a career renaissance as he played a couple clips under a point-a-game in the regular season then was one of the Devils best players en route to a Stanley Cup.
That was really his last great moment, though, as the following year his offensive game dried up and the Devils missed the playoffs. His final NHL season was a turbulent one, as he went from New Jersey to Los Angeles then back to Dallas. A return to big D appeared to work wonders as he played much better than he had in the last year-and-a-half. However, the Stars only used him sparingly in the playoffs and when he couldn't find another team to catch on with in the 1997 off-season, he finally called it a career.
Broten himself says he was a good player but never a great player. I think he is being a bit modest. True, he was never the best player at his position at any specific time in the NHL, but there were certainly times where he was great. Being the first American-born NHL player to hit the 100-point plateau must count for something. His performance during the 1991 and 1995 playoff runs he was a part of were both great as well. His 1991 performance in particular is often overlooked, especially in the opening round against Chicago and the finals against Pittsburgh.
Mind you, he's always been one of my favourite players, so I may be a bit biased.