Although most of what I (and the majority of people) have to say is totally anecdotal information, there are a few definite, normative facets to DK's game:
1. Projectiles are hard to counter. Yes, you can hit most of them, or Short Hop Air Dodge in order to approach. These tactics are not only difficult to implement, but also easy to read and counter by the opponent. So, campy characters give DK a larger problem than they give most characters.
2. Bair, Bair, Bair This is, in my very humble opinion, DK's best move. I am willing to purport reversed Bairs as DK's best approach method, and maybe his best tactic overall. Not only does this ability have an insane hitbox(long, and almost above DK's head), it also can scoop opponents off the ground.
3. His Nair kills at low percentages Pretty self-explanatory. Get an enemy high enough in the air, and DK can vertically KO just about anyone that isn't a behemoth (Bowser comes to mind.)
4. Chain grabs Like many people have said, chain grabs destroy DK's large frame. DDD can murder the poor primate with his chain grab. As aforementioned by others, DK seems to be at a severe disadvantage to DDD, ICs, and other chain-grabbers.
5. Spacing An aggregate of Numbers 2 and 4, spacing is absolutely imperative to DK's survival. Although it can be concieved as "cheap", a DK's best bet in many a scenario is b-air camping, with intermittent F-tilts (incredible range) and some D-titls. This is necessary to ensure enough damage to use killing moves, and to deny the opponent the ability to rack up combos on DK's large frame. Characters with large reach (Marth, Ike, Zamus) have several options to mitigate this, so DK's spacing advantage can become all but void.
6. Strength DK's calling card is his propensity for killing at low percentages with his beastly array of muscular moves. His Forward smash is powerful, and his charge punch packs some mean killing potential. This affords our ape-protagonist a serious advantage over light, flimsy characters ranging from Jigglypuff and Kirby to Peach and even Pit.
I hope this helps in everyone's considerations and deliberations regarding specific character match-ups.