Any major professional sport. My list is kind of slanted:
Baseball
Dodgers, Padres, Giants, Rockies, Diamondbacks (all at either Petco or Dodger Stadium), Mariners, Reds, Royals, Angels, Pirates, Cubs, Brewers, Cardinals, Braves, Twins, Mets
Basketball
Lakers, Celtics
You?
Only baseball. 11. Yankees, D-Backs, Giants, Angels, Tigers, A’s (when they were KC), Twins, Cardinals, Expos, Red Sox, Blue Jays. I think that’s it. All in 5 parks: Tiger Stadium, Comerica Park, Bank One Ballpark, Edison Field, Busch Stadium II.
NFL
Chargers, Broncos, Dolphins, Rams
NHL
Oilers, Kings, Canucks, Leafs, Jets, Bruins, Senators
NBA
Lakers, Raptors, Nuggets, Hornets
MLB
Twins, White Sox, Athletics, Padres, Reds, Expos, Phillies
CFL
Everybody 
Hockey:
Hurricanes and whoever they were playing that day 7 years ago
Baseball: Home Parks–Yankees, Mets, D-Backs, Dodgers, Angels, White Sox, Cubs, Red Sox, Rangers, Padres, Marlins, Braves, Brewers, Phillies. On the road– Indians, Reds, Pirates, Blue Jays, Mariners, A’s.
Basketball:Home– Knicks, Kings, Lakers, Suns, Magic, Spurs, Nets. Road– Bucks, Bulls, Blazers, Clippers, T-Wolves, Nuggets.
Football: Home–Jets, Giants, Cardinals (AZ), Bucs, Falcons. Road– Packers, Bears, Dolphins, Oilers, Chiefs.
Never been to a hockey game.
As a lifelong Yankees fan and native New Yorker (albeit one who left New York in 1986), I’ve gone to Yankee Stadium countless times and have seen every team in the American League play there, except for one: the Tampa Rays/Devil Rays.
And I went to enough Mets games to have seen every National League team except the Colorado Rockies and Washington Nationals.
In the NFL, I’ve seen actual regular season games involving the following
Buffalo Bills
Dallas Cowboys
Houston Oilers
New England Patriots
NY Giants
NY Jets
San Diego Chargers
Tampa Bay Bucs
Washington Redskins
I also got to see an exhibition game featuring the LA Raiders, who trained here in Austin with the Cowboys one year; Al Davis was an interesting guy who refused to sign autographs (his attitude was, if I sign for one person, I have to sign for hundreds of other people, too, and that’s too much work) but was happy to converse with fans at length. And Jerry Jones, who had just recently bought the Cowboys, tried hard to give his autograph to everyone i ntown, whether they wanted it or not!
In the NBA, I’ve seen:
New York Knicks
Chicago Bulls
Portland Trailblazers
San Antonio Spurs
In the NHL, I’ve seen:
Boston Bruins
Minnesota North Stars
New York Rangers
MLB: the Orioles and anyone they played at home from 2003-2006.
NFL: Redskins, Ravens, Cowboys, Eagles, Giants, Cardinals, Colts, Bolts, Bucs, Pats, and a really long time ago, the Oilers.
NBA: Wizards, Nets, Heat, Pistons, Knicks.
NHL: Caps, Pens, Flyers, Devils, Canes.
MLS: DC United, Wizards, Metrostars, a few others I can’t remember.
Baseball: Hard to say offhand. As a long time (well, 10+ year) partial and full season ticket holder for the Mets I’ve seen every team that’s come to visit Shea/Citi Field, which would mean all 16 NL teams plus the now defunct Expos. Also most of the AL teams that have come to play at Shea/Citi Field for interleague games: the Yankees, Rays, Orioles, Red Sox, Twins, Royals, Angels, A’s and Rangers (though it ultimately got rained out). And this year I’ll also see the Tigers for the first time in person (yippee-kay-yo). I’ve seen the Yankees take on the Mariners at Yankee Stadium too. So not counting the Tigers just yet (until Thursday), that makes my count of MLB teams 27.
Basketball: until about 2002 I used to go to 10-15 Knicks games a year, including some on the road, and have seen them play against all but the newer relocated or expansion-added teams. Of the 30 current teams, I haven’t seen them play the Bobcats or the Thunder, but have seen them play against the Supersonics; and have seen them play the Hornets and Grizzlies while in their original franchise locations of Charlotte and Vancouver. So call that 30 minus 2 plus 1 = 29 NBA teams.
I’ve never been to a pro football or hockey game.
I had season tickets for over 20 years at Tiger Stadium, then the Silverdome for the Detroit Lions . I went to 15 (ave. Detroit Tiger games a year for 20 years. I have gone to lots of basketball games for the Pistons, first at Cobo then in Pontiac. I had a friend who worked at the Red Wings and I went to a lot of hockey games for the Red Wings. I went to the Silverdome for the Michigan Panthers ,when they had a football league competing with the NFL. (USFL) I have seen a lot of sports in person.
They are all better on TV.
Football: Raiders and whoever they were playing the day I saw them.
Baseball: A’s and whoever they were playing the two different days I saw them on my company outing.
Hockey: Sharks and whoever they were playing the several times I’ve seen them.
NFL
I’ve gone to one or two Packer games per year since around 1977 (my family has season tickets). I’ll undoubtedly miss some here, but the teams I can absolutely recall seeing play:
MLB
I’ve gone to a half-dozen or so Brewers games, at least that many White Sox games, a few Cubs games, one Twins game, and two spring-training games at the Pirates’ place in Florida. This is an even more incomplete list, as I don’t recall a lot of the opponents in those games:
NHL
I’ve been to two regular-season Blackhawks games, one pre-season Blackhawks game (don’t recall who they played), and one game for the long-defunct Chicago Cougars in the WHA in 1974 or thereabouts.
NBA
I’ve been to one Milwaukee Bucks preseason game, around 1978 (they often play one pre-season game in Green Bay, where I grew up). No idea who they played in that game.
I’ve been to probably about a dozen baseball games over the years, but can’t possibly remember who played. The home teams were the Padres, Giants, or Yankees, but I couldn’t tell you anything else (and am kinda amazed that others would be able to remember those details).
NFL: Cards when they were from St. Louis, the Colts when they were from Baltimore, the Oilers when they were from Houston AND Memphis, Titans, Cowboys, Redskins, Eagles, 49ers, Ravens and Browns.
MLB: Nationals, Orioles, Cubs, Cards, Mets, Phillies, White Sox, Mariners, Brewers, Padres, Royals, Rays, Braves, Reds and maybe one or two I forgot.
NBA: One Wizards game against Golden State or somebody that they, of course, lost.
NHL: The Caps, Lightning, Rangers (?), Penguins
Twins. Rays. A’s. Giants. Braves. Cubs. Astros.
Sixers. I can’t remember who they played. It was an exhibition game anyway.
And that’s it. Only two of them were in my adult life; Twins at Rays during a bachelor party and I scalped a ticket for the last three innings of Astros at Cubs when I was visiting Chicago. I’ve seen tons of college teams play though, I don’t really care for pro sports and their exorbitant ticket prices.
Don’t remember them all:
Baseball:
Red Sox, Yankees, Angels, Twins, Cardinals, Royals, Cubs, Diamondbacks, Mets. There are others, but I don’t remember all the road teams. I’ve been to games in Boston, Chicago, St. Louis, KC, and Minneapolis. I’ll be seeing the Rays in Boston in a couple of weeks.
Football:
Rams, 49ers.
Hockey:
Blues, whoever they were playing that day.
I’ve seen in person about 70 different professional baseball teams. My ticket stub album shows about 65, but there’s a few missing.
I saw the Giants lose to the Eagles in an unwatchable 9-6 trainwreck.
I saw the Jets beat the Dolphins in the Midnight Miracle, and I stayed to the end. (Links go to the NFL Films special about the game, split into two parts on Youtube.) I screamed my throat bloody raw that night, and showed up to work several hours late the next day to an incredibly jealous boss.
I’ve gone to 3 or 4 Rangers games at MSG; no memory of who they were playing.
That is a really tough question, without a stub collection (nice work there, sparky!).
Football: Chiefs, Raiders, Bills (maybe), Bengals, Colts, Texans
Basketball: Kansas City Kings, some other team, Pacers, Bulls, Heat
Baseball: Royals, White Sox, Cubs, Nationals, Phillies, Reds, Padres, Mets, Marlins, Rangers, Brewers, Indians, Twins, Orioles, Angels, Red Sox, Yankees, Mariners
I’ve been to six or seven Cubs games, one Bears game, two Blackhawks games, four Bulls games. I couldn’t tell you what other teams were present if you put a gun to my head. I’d guess between 15 and 17 teams total.
In hockey, I have seen the Maple Leafs vs. the Red Wings, Canucks, Stars and Lightning; and the Senators play the Rangers. Strictly speaking, the OHL Peterborugh Petes and Sudbury Wolves aren’t professional, but the players do draw a nominal stipend; enough to make them ineligible for NCAA play.
In baseball, I’ve seen the Blue Jays play the White Sox, Royals, Brewers, Rangers, Orioles, Tigers and the Athletics. I’ve also seen the minor league (AAA) Ottawa Lynx play the Scranton/Wilkes-Barre Phillies.
And I’ve seen the Toronto Rock play the Buffalo Bandits in the National Lacrosse League.