I'd like to have some sort of cover system really. Thats what I hated the most about the others. As long as it stays deliberately over the top I'll be happy though,

Fix the vehicle physics and sound effects. It would also be nice if they didn't hold back so much apparel. OH! And stop repeating voice clips. I almost went insane from the French bitch in the septic truck. It's time for a new city as well.
 
I don't think a cover system is needed because you can just move behind stuff and crouch if you need to. The game isn't exactly hard in the first place. I'd rather current problems be fixed before adding new features.

Hire new writers and artists for the game.  The gameplay mechanics are great, but those two aspects of the game are appalling.
 
If only Volition and Rockstar North can combine to make the perfect free-roaming crime game.

Make sure the game feels free-a plus that was for Saints Row 2, and, in my opinion, not in GTAIV.

I loved Saint's Row 2, but there are plenty of things that I wouldn't mind seeing changed and/or improved. A new city (which seems likely) and some tweaks to the overall art direction would be great. In addition, some of the vehicle physics did seem a bit odd at times so it would be nice to see some of that addressed.

The return of the female voice actor that sounds exactly like Beyonce
Less minigames, pick a few but really polish them up 
Fix PC performance issues

Better missions than "Go to A Kill B".

A whole new game. Whole new game. Just start over from scratch, and try to put a somewhat serious spin on it. Not going to lie, its wackiness was a good welcome, but I thought it was just too wacky.

Better voice actors for the main characters, I ended up playing as a "White female" because she was the only one who had a good voice, although, she WAS pretty badass.

I thought the Latino Male was an awesome voice. Came up real great when you put him in a sharp suit with a good Mustache.

more explosions. the explosions were awesome in SR2, and i want more of it

I'd love to see some of the stuff they already have bolted down in a more serious way, but still retain the majority of it, I felt they might have spread themselves a little thin in the 2nd, it was a fun game, but it felt a little shallow, little things like the shooting could be a little better, the way the character was within the environment was a little dodgy for me in spots aswell.

How about a decent port to the PC?

Not landing like a retard after a jump.

Less needless stereotypes. Better acting. In general, better gameplay mechanics.

• A complete overhaul of the engine. Often (on X360) the game's FPS would drop to literally nothing. Water effects, explosions, and generally too much happening on the screen just made the game unplayable from time to time. And even after the update the game crash every now and then, which is just mindblowingly annoying.
• Better physics. I can't really describe it well, but it feels objects and especially vehicles didn't perform well. When you crashed into something you got stuck way to easily, not to mention when other cars ram into you they seem to "stick" to you.
• Improved AI. One thing that really bugged me was the AI's ability to often drive their cars almost flawlessly. In a high-speed chase it's not really realistic to have the ones chasing you (or the one you're chasing) to drive like gods, when you yourself manage to ram into objects and other cars far too easily.

Camera angle in car was a bit gay if you had a weapon out.

 
better customization

New ethnic selection like Middle Eastern and Native American and other accents like London English, German, Irish English, French, Scottish English and so on.

The driving really needs to be improved. Not like I was against its arcade driving style but it was just...a really bad arcade driving style. Little sense of speed. 

The opposite of GTA IV in terms of "New Direction"
More accents, like the user above said but without so many fucking English's 
Irish Accent being most important, with variations to dialogue such as: Fuck becomes Feck, Ass/Arse, Shit/Shite and so on.
 
4 player co-op 
More customization, add certain parts onto your crib like number 2, but to the outside. New Garage, second floor etc

i would love to see that dam hair glitch gone but really i just want to see gat go nuts and kill people all over again lol

Everything changed. I liked the wacky idea, and customization... but really get rid of the stereotype attitude and writing.. work on the god-awful gameplay mechanics, and you may have something there. To me the 2nd one felt like a poorly executed, obnoxiously written version of a San Andreas knockoff. That said, I do still think there's room in the market for a "over the top" sandbox game, and I think Saints Row 3 could be that answer. While I wasn't crazy about the last 2 games.. doesn't mean that the developers don't have something to offer.

Less jank, more polish.

as long as i can keep my sexually questionable bone-skinny with boobs and a pink beard and girly hairstyle with a pissed off british voice character, i'll be happy

Lose the MADTV style humor.  It's extremely grating.

Fix the multiplayer so it's fun to play

"

The return of the female voice actor that sounds exactly like Beyonce

"

I'd like the car despawning to be a little less severe. It's especially frustrating when you're trying to do chop shop, and you pan the camera around for a second, look back, and the car you were chasing that was not much more than a couple of feet away has despawned.

Level of customization was great in SR2...now make it even better.  Ten times the clothes, body mods, tats, hell, bring on full nudity even.  I'd say take that attitude to your pad also...it felt weird to me only having like three decorating options for your safe houses.
 
KEEP the irreverent wackiness.  Don't make it more serious.  Trying to be all serious and artsy is the hallmark of a GTA game, and the last one of those sucked ass.  If I wanted maturity I wouldn't be playing a video game. 
 
Bring back Eliza Dushku as a voice actress.  She is so hot even her voice is sexy. 
 
Keep the crazy minigames and offer even more.
 
More crazy sidequests.
 
Try to make it even more violent and sexy.  My fantasy is that people on the extreme right and extreme left find common ground over wanting this game banned.
 

" Camera angle in car was a bit gay if you had a weapon out. "

More framerate. Less jank.  
 
But I hope they don't change the explosions. I like the way stuff blew up real good in the first two.

Please go back to a funny gangster game like in SR1, as opposed to a ridiculous gangster game in the second  
atleast thats how i felt about sr2 
both good 
both favorite

i'll have a high end PC by then and will max out Saints Row 3, instead of the low settings im rocking in SR2 right now.. 
 
what would i like to see? i dunno. this franchise is crazy and fun, i dont have any demands or complaints, i just roll with it

More guns and better gunplay.
And i hope it won't have the same frame rate problems the second one had for the PC.
But im sure its gonna be one hell of a ride.

I want this game to be so crazy that it makes Saints Row 2 look like GTA IV in comparison.  Also it must bridge the gap between the Saints Row universe and the Red Faction one so we can get a crossover game that features gang bangers tagging on Mars and space miners knocking down buildings in the ghettos of a made up Florida city with sledge hammers.

Fixed vehicle handling and frame-rate.

Purpler cars.

Bigger, better, crazier.

A hot coffee controversy

Dear god I do not want a cover system in Saints Row, it's just not for this series. 
 
As long as SR3 continues to add more customization, more vehicles, more weapons, and more crazy shit then I'll be happy.

I want this: 

" Take a tank skydiving, call in a satellite-targeted airstrike on a Mexican wrestling gang, and defend yourself against a highly-trained military force using only a sex toy in the most out-landish gameplay scenarios ever seen, igniting a city-wide war that will set Steelport on fire. Strap it on. "

I just want more saints row. It would be nice if they could find the balance between saints row 1 and 2, I hope they don't go even more over the top just for the sake of it.

More polish.
Much more polish.
And hopefully a better PC port.
 
If Saints Row gets to the level of quality of GTA series at least but keeps the craziness, it could be the best thing ever.
If SR3 goes beyond that and does a better job with controls and optimization, it would be fucking awesome.

More missions that involve covering the entire city in liquid hot shit.