A lot of awesome suggestions so far! My list is kinda TL;DR, but I'm doing it to organize my own thoughts as well; here goes!
Some people have already said this, but:
- More gangs. Italians and Russians get boring after a while. I like the Chinatown Wars setup, where there's like 5 or 6 gangs, and each of them have clearly demarcated albeit sometimes overlapping territories, creating the possibility of player-independent conflict. Sometimes, I just like watching people shoot each other while I run around, cover and watch the action. It would be cool to video record somehow!
- The drug-dealing mini-game in Chinatown Wars should DEFINITELY make a comeback. I think I spent more time on it than on the actual game itself...
- BUYING STUFF. Exorbitantly expensive safehouses give you a reason to hoard money. There should be a LOT more clothes. Different foods should replenish varying amounts of health, as in SA. More hair cuts and appearance customization. There should be more styles, like Goth, Emo, Gangster, Scene, Metro, etc. There should just be MORE stuff to spend your money on, in general.
- Maybe an electronics store? Could sell different models of phones and Media Players. Say the crappiest one could store like, 5 songs, and the best one like 100. Phones could have different features.
- Stuff to put in your safe houses. Bongs, TV's, Stereos, Pipes, Computers, Paintings, maybe even have an Interior Decorator who you can hire through CrapList to customize your walls, floors, lights, fixtures, and furniture or something?
- MELEE WEAPONS. C'mon, at least 5 different ones. I want katanas and dildoes! (no homo)
- More Asians.
- More Asian girls. (Not azn or anything, just noticed a serious lack in GTA IV)
- More prostitutes! (Plz no more fat black ones R*)
- VIOLENCE! I remember in the PC version of GTA III (or was it Vice City?) you could blow people's arms, legs, and heads off. I was 10 years old when GTA 3 came out and haven't played it since then, so I may be mistaken...but come on, it's already rated M, give us more freedom to mutilate our victims!
- Damage detail. GTA IV really hit the nail on the head with this one.
- Drug USAGE!! You can already get drunk. In Saint's Row, you can get high...why not simulate the effects of other drugs? Obviously, none of them will be realistic or even give the slightest hint as to what actually being on drugs in real life feels like, but it can still be fun. Just imagine some really creepy, yet eerily beautiful color and audio distortion whilst under the effects of Magic Mushrooms! On weed, time could slow down at random moments, and maybe the controller could start pulsing randomly, when you feel your heart beating through your whole body!
- Many different avenues of making money. Assets from VC, Territories from SA, and Drug Dealing from CW should all be featured.
- Martial Arts training.
Welp, those are just the ones off the top of my head that I really want to see. Nothing I've said is really new, and everything listed is DEFINITELY doable (for the PC at least hehe). I want GTA IV+ graphics combined with SA options and customization.
Finally, one thing I thought off that would be cool would be an extension of the dancing minigame...you'd be able to either turn up the car stereo really loud or buy a boom box (at the aforementioned Electronics store?) and then just set it down somewhere, tune it to your favourite song, and start up a dancing mini-game. If you're doing it really well, maybe you could get a little crowd forming a circle around you on the street. Maybe girls would want to follow you back to your car, maybe people would throw money at you as you dance? Who knows, it'd be fun though
I would be very supportive of a female protagonist, if they managed to pull it off right (ie no gangsta girls please...) Or even better, multiple characters throughout the story who have interwoven plot lines (some become friends and can use each other's safehouses/assets/territories/w.e...dunno how it would work, would take a lot of thinking and planning really)