This is likely to be a long post, so I'm going to be as succint as possible with each aspect of the game and how I'd streamline things.
Races
1. +2 bonus to an attribute, determined by race. Most only have a single favored attribute, but some could have more than one that you can choose to raise. Humans can give the bonus to any attribute, but they have a maximum starting attribute score of 18 in all attributes.
2. Bonus feats (maybe 2), also determined by race. Probably at least 2 options for these. They'd mostly be generic, skill-based feats. Humans would have the most options, but they wouldn't have every feat available to them. I'd probably give them choices from the skill-based feats, the weapon proficiency feats, and the feats that boost saves or HP.
Classes
1. Start off with generic classes, with the base classes being for adventurers. Talent trees instead of class abilities to give more options. I have a write-up of what I had in mind for this on another thread, but I can't use the Search feature to bring it back up. Of course, I'd definitely modify these things heavily to make them less cumbersome for a more streamlined D&D.
2. Multiclassing penalties are based upon the number of additional classes taken and how divergent they are in concept, not on how far apart they are in level. It should be easier for a fighter/barbarian/ranger to keep advancing than it would for a fighter/rogue/sorcerer. Monks and paladins, instead of losing the ability to advance in the monk or paladin classes, gain a multiclassing penalty. No multiclassing penalties for generic classes. Multiple prestige classes incur a multiclassing penalty.
3. Most alignment restrictions dropped, except for the case of druids and paladins, possibly monks.
4. Make the base skill points be 4 + Intelligence modifier (x4 at 1st level). Very skilled classes would have more.
5. All classes are proficient with simple weapons. Armor and martial weapon proficiencies (if any) are based on class, with fighters getting the most. Maybe incorporate the weapon group proficiencies from UA. Or go back to AD&D's proficiency system, where classes get a certain number of weapons to be proficient in. Of course, they wouldn't have the same number of weapon proficiencies as their AD&D counterparts, but the idea is the same.
Skills
1. Completely do away with the class/cross-class skill distinction. Have only the number of skill points based on class (as well as the character's Intelligence modifier) be the limiting factor in how skillful a character becomes.
1a. Alternatively, give players more options with class skills, but redo the skill rank maximums. Ideas include: absolute maximums (only a certain number of ranks per skill period, no matter what level; i'd say 20 is good); maximum ranks based on level (as in PHB, but regardless of whether a skill is a class or cross-class skill); class and cross-class skill maximums, but have the max for class skills be level +5 and the max for cross-class skills be equal to your level.
2. Simplify the skill list to: Acrobatics* (Dex), Athletics* (Str), Awareness*, Concentration, Craft, Disable Device* (Int), Gather Information, Handle Animal, Heal, Knowledge, Navigate* (Int), Observe* (or Notice), Perform, Persuade* (Cha), Profession, Ride, Sleight of Hand, Speak Language*, Spellcraft, Stealth (or Sneak), and Survival.
2a. Acrobatics is Balance and Tumble combined.
2b. Athletics is Climb, Jump, and Swim combined.
2c. Awareness is a skill I made up that was once Sense Motive. Unlike Observe, it is more subtle and used for sensing things that go on beneath the surface. While Sense Motive is used purely for social interaction, Awareness has broader applications. The detect spells could give a bonus to Awareness checks in certain situations. Awareness, however, is no substitute for telepathy or clairaudience/clairvoyance or scry.
2d. Open Locks is folded into Disable Device.
2e. Though I do not lament the loss of the Intuit Direction skill in 3.5E, I think that there are uses for navigation besides the wilderness.
2f. I realize that blending Listen and Spot into Observe and Hide and Move Silently into Sneak could make bards, rangers, and rogues more powerful, given that they can not only maximize their specialty skills, but also branch out into others as well. Reducing the number of skill points these classes get by about 2 might work, especially since you no longer need to distribute points amongst 4 different skills to be good at observation or stealth.
2g. I have combined Bluff and Diplomacy into Persuade since the means and ends of both these skills are very similar.
2h. As someone who has learned (and forgotten) foreign languages before, I think there is merit to the idea of having ranks in language skills. The number of ranks does not determine how close to native fluency you speak, but how well you can express yourself in that language. Native fluency would be somewhere between 10 and 15 ranks, and given for free for your character's native tongue. Bonus languages would be around 5 ranks. It's one thing to communicate basic, factual information in a way that can be understood and quite another to express complex, subtle ideas. Language ranks should give literacy based upon the standard level of literacy for the world. If literacy is rare and precious, writing and reading should be based in Craft (writing) or something.
Feats
1. Since the skills will be changed, most of the skill-based feats will change as well. Several of these would be shifted to the Skill Focus feat since the bonuses given would be in skills that have been folded together.
2. Combat feats should be designed more like Combat Expertise and Power Attack. They are simple to implement, easy to remember, and remain viable at all levels. I'd rather have fewer feats I could use in this way than a lot that are only applicable in very specific situations. Better feat design could do much to streamline combat as well as to make fighters the supreme combat characters.
Description
1. Alignment should be dropped or replaced with the allegiances from D20 Modern. Too many times alignment is used as a straightjacket for a character's behavior and personality, rather than a descriptor of her general characteristics.
2. Deities should be dropped or replaced with a concept-based create-your-own deity toolkit. I had an idea for a revised cleric I had called aspects, which basically determined what a deity was god/goddess of, rather than trying to shoehorn specific deities into campaigns that may not fit them.
Equipment
Nothing to change here.
Combat
1. Combat should be heavily modified, sticking to the basic formula as much as possible. Having rules for so many maneuvers and situations that can crop up just bogs down the system and is often best left as a DM judgement call. I know that many of the things in the combat chapter of the PHB are optional, but I'd rather these options be detailed in another book. You could even add the entire content of the Miniatures Handbook in it and get a good amount of optional rules and expansions to play with.
1a. Instead of all these tactical options which may or may not be desirable for every group, I'd prefer it if we had rules of thumb based on advantages and disadvantages a character faces in any given situation. Advantages give circumstantial bonuses, and disadvantages give circumstantial penalties. The basic scale of advantages and disadvantages would be minor (+/-1), moderate (+/-2), signficant/severe (+/-5) or extraordinary/crippling (+/-10).
1b.The good thing about this is that it can be used outside of combat too. Trying to Sneak while in an open field in the middle of the day while surrounded by elite troops would put the character at a crippling disadvantage.
2. No need for battlemats!
Magic
1. Nix the arcane/divine magic divide. Magic is magic is magic. The difference between casters should be more along the lines of how they focus and channel magical energy. Mystics do so by attuning themselves to the world around them and letting things flow from that. Magicians do so by willing things to happen.
2. If you're going to have different spell lists, base them on the archetypal magical types rather than domains or schools of magic. Black magic, white magic, and green (or nature) magic are all things I've seen countless times in fantasy novels and films. Enchantments and illusions (which I call fey magic in my own write-up of a generic spellcaster) are also a common motif. Magic based in the 4 basic elements (fire, earth, air, and water) is also common. Not to mention the seers, prophets, and diviners that abound in mythology and folklore. I have never come across an Abjurer or Transmuter aside from D&D. It's a lot easier to pick spells that make sense for a character, even if a newbie, when you get a general idea of a theme or motif around which that character casts, as opposed to the anything-goes sort of thing that is common for D&D.
3. Metamagic should be worth sacrificing a feat.
I think that's about it.