Well, let's start it off I guess.

1) Tom Brady on the cover: Let the curse begin, bring down the Pats.
2) More appropriate application of stats: When you look at them, sometimes it just doesn't add up. Take Mike Alstott for example, in real life, he runs like a freight train, but in Madden, he can be brought down by somebody like Michael Hawthorne. Same application with running backs who tend to loose the football.
3) Better design with sweep plays: I don't know if this is just me, but sweeps seem to never work for me.
4) Penalites: Helmet-to-helmet contact would be great, even though you are flagged for them. (To me: If it happens in the NFL, it happens in Madden.) Illegal touching, I.E. If a player steps out of bounds and them comes in, and is the first to touch, Defensive holding, offensive pass interference, and the like.
5) Challenges: I've had touchdowns where the reciever had one foot out of bounds, and he was STANDING, and the play was reversed for a touchdown.
6) Celebrations: Much like in NCAA 2005, they should incorporate more celebrations, and user-initiated celebrations. They should throw in the Dirty Bird, Colts-Bumping thing, '85 Bears high fiving thing, and a much better Lambeau Leap.
7) Better drafts: This has already been well covered by most people
8) Online Gameplay*:
A) Stat-ticker: Maybe a ticker-type thing that pops up, showing who your buddies are playing against, what the score is, that sort of stuff.
B) More minigames: Personally, I felt that the RB drill was a very clever thing put in, and that they should try to incorporate more into online gameplay.
C) The ability to challenge a call: Haven't we all had that experience before?
D) Stricter Depth-Chart restrictions: If in life, the starting QB for whatever team is not playing that week because of an injury, they should make it so that online players cannot simply go back into depth charts, and put him in because in Madden, he can play.
E) More frequent Roster-Updates: This may sound like a bit much, and I can understand how time-consuming it can be, but this is only a request.
9) Home field crowds: I think this, also from NCAA 2005, should be incorporated into the gameplay of Madden. A great idea, bring it to the Pros.
10) Indoor/Outdoor advantages: Give player boosts when they are in situations where they actually show an advantage. I.E. Up the Rams' Player's speed when they play home. They are so much faster on their turf than outside. Or Green Bay when the weather is below freezing, seeing how dominant they are when that happens, or Green Bay in the playoffs at home. A downer would be Favre in a Dome. That sort of thing.
11) Match-up Stick: Again, another invention from NCAA 2005, I believe it could find a good home in Madden '06.
12) Sleepers: Why can't a 6th round pick in the draft turn out to be a 1st-rate stud?
13) Different commentators - different days: While this may not pretain towards Madden itself, I believe that they should have John and Al commentate when games are played on Monday nights, and Thursday special occasions, and then bring in other commentators for different games. IE Joe Buck, Collinsworth, the Fox Crew for regular Sunday games, and Sunday nights would entail the ESPN crew. ((I know this would infringe on other company's and other titles, but I actually think it would up the gameplay of the game that much more. Because how tired do you get of John and Al, every game?))
14) Player Suspensions/ Off the field activities: Koren Robinson, point right there. Why can't there be infractions off the field that require Coach-punishment?
15) Better running game: Being able to jump over the pile, push the pile forward by dropping the shoulder and trying to churn out yards, and all around, try and make it so that sometimes it's the Runningbacks that are dishing out the pain as opposed to the secondary and linebackers.
16) Better passing game: Make it so that different recievers run some routes better than others, that sort of thing, or are better blocking recievers than others, IE The Blitzburgh recievers
17) Player Egos: While this isn't really important, it would add to the realism of the game, like TO taunting the secondary, or Ray-Ray making the big stop and doing his classic dances. There has to be more interaction in my mind between players, really capture their mannuerisms.
18) Indepth injuries: I remember in like, Madden '97, the little ambulance would come out and pick players up. Now, somebody would break their leg, and walk off the field holding their arm. I think that they should make it so that when a player sustains a serious injury, he needs to be helped off the field by a cart, and that he should be shown going to the locker room.
19) Half-time shows: Hey, if ESPN 2k5 could pull it off, why can't Madden?
20) Post-game shows: Same concept, draw it out further.
21) Gamebreaks: Again, show what's going on around the league.
22) Hot and cold streaks: Teams get into funks and grooves, IE Pros: Bills, Packers, Steelers. Cons: Minnesota, San Fran, Miami
23) Players comming out of retirment: Well, you look at it, players sometimes do. Deion did it, just like, a one-year stint. Cris Carter did it. Granted they wouldn't be that great, but it'd be fun to see them lace 'em up again.
24) Contracts: Already been covered.
25) Rotation of game refs: Not really a necessity, but it would add to the realism again, if we saw different refs now and then. And they could even have tendencies, like known to be bad judges, or good ones. Make insane calls, or good ones. Do we have to go back to the Washington-Dallas MNF game to see bad calls?
26) Practice squads: Again, already covered.
27) Practice weeks: Able to boost player abilites during season, granted it would be much harder, because if it was too easy, you'd end up with a 99 rated team by the end of the season. But with that, you must also risk injury, seeing as that does tend to happen during practices too.
28) Better spotting of the ball: How many times have I seen Green get stuffed, but fall forward passed the line, and have the ball spotted before it?
29) Forward progress: Ties in with the penalites and previous statment.
30) Hard-counts: Some QB's tend to make a hard count better than others, like Brett Favre's classic "Walk away from the line, then get back and snap it" one. I think that could help.
31) A bit of an upgrade in ability points: Some people do have a tendency to get angry with the application of speed, and sometimes I don't blame them. Sometimes I find myself scratching my head at how the hell that play happened.
32) Better physics: How can a linebacker, with his back to the ball, know suddenley when it's comming and able to swat it away? DB's sure, but lineman and linebackers are a bit questionable.
33) Better application of tackling: Have players record half-sacks, assisted/non-assisted, and in often times, having the player grab somebody around the wasit, but lack the power to bring them down, so they drive them out of bounds.