Ultimately, a character can't do anything unless the DM approves
There's no game without both the DM and the players. I'm really not trying to state the obvious here, but it's true. Characters don't exist until a setting's been provided, and many choices that influence character creation and development come from the setting the DM supplies, and that includes details like what's for sale. If a character's created in a setting vacuum as a mechanical or narrative exercise, there's no rule that says the DM must allow that character—as it exists and without alteration—into the DM's setting even if the character's been created using the Player's Handbook exactly as written.
To make sure of this, I reread the opening pages of the Dungeon Master's Guide for Dungeons and Dragons 3.5 and it says
Every Dungeon Master is the creator of his or her own campaign world. (6)
Good DMs know not to change or overturn a published rule without a good, logical
justification so that the players don’t rebel... (6)
So if the world the DM creates doesn't follow the all the rules, then the DM's overturned one or several published rules, and let's hope he has a good, logical reason for it. As a potential player in such a campaign, your choices become play, negotiate, or walk.
That means if the DM says, for example, No elves because the DM's created a world and overturned the rule that elves are an allowed race for PCs, you either don't play an elf, try to talk the DM into letting you play an elf anyway, or leave the table.
Note that overturning the rule that allows characters to purchase any item priced at 3,000 gp or less, and, instead, mandating players seek the DM's approval for non-Player's Handbook purchases isn't particularly onerous as house rules go. That's not the DM being a controlling jerk; that's the players being courteous.
I'm pretty sure this isn't the answer you're looking for. You might want a hard, fast list of what, specifically, must be approved by the DM and what need not be approved by the DM. Unfortunately, there is no such list nor can there be. The game contains multitudes, and each DM will have an individual list.
Used wands are specifically addressed
The Magic Item Compendium on Used Wands says
Particularly when equipping an NPC, affording a fully charged wand can be difficult. Since the typical NPC won’t have a chance to use more than a few wand charges in any combat, consider equipping such characters with partially used wands—that is, wands with fewer than full charges. This is also a good way to put a cheap wand into a treasure hoard, and you can even allow PCs to select a wand or two this way as well. (227)
Emphasis mine. So, while this is mainly about equipping an incoming NPC, there remains the option for the DM to allow PCs access to partially-charged wands, albeit to a limited degree, and, arguably, such PCs should also be new to the campaign.
Why limit used wands?
I recommend keeping with the Magic Item Compendiums suggestion of "a wand or two." That's because it's difficult to justify the existence of a marketplace containing the partially-charged wands the PCs want, and, from experience, the game is unbalanced by making partially-charged wands readily available.
A creature can, using a rather obscure method, create a 1-charge wand, but, whether because of the level 11 minimum or because the DM disallows Web material, such items probably won't be available in most campaigns.
Creating 1-charge wands
A creature that wants to create a 1-charge wand acquires a staff of the spell then casts repeatedly on that staff the obscure 6th-level Sor/Wiz spell The Hamagess' staffsprout [trans] (Mintiper's Chapbook Web column "Part 10: Chronicler's Compendium"), each casting creating a lone 1-charge wand but, likewise, depleting the staff of 1 charge.
One-charge wands created in this fashion have at least a caster level of 8. Further, unless the staff's creator was or had help from an appropriate creature with unusual casting (e.g. a guardian naga, a blue dragon), all such 1-charge wands will be exclusively of common arcane spells. Finally, to cast a 6th-level spell a Wiz11 typically charges 660 gp, and that amount should be added to the cost of any 1-charge wand manufactured in such a manner.
Were there a valid non-adventuring use for the first 49 charges of a wand, 1-charge wands could become available. For example, in a campaign setting wherein a vast organization of creatures is constantly feeding the planet spell energy to keep the planet alive, servants might swipe nearly exhausted wands and sell them for beer money, knowing their masters weren't going to miss that last charge. But, as can be seen, that's a huge conceit to justify the existence of one kind of not normally available magic item.
Were a creature to develop a cheap, efficient, reliable way to make partially-charged wands, as KRyan points out in his answer, the market for many potions and over 1/3 of scrolls would dry up overnight. There're a handful of reasons to use either kind of now-obsolete item—just as one can still use an adding machine, pager, or typewriter—but partially-charged wands would displace most of those difficult-to-use magic items like the mobile telephone's replacing the landline. This isn't a bad thing—and could form the spine of an interesting magical-industrial revolution campaign—, but for most campaigns, verisimilitude will suffer if the DM fills shops with 1-charge wands yet determines treasure randomly or uses published adventures, the game still expecting and providing a mix of magic items.
Also, if you're playing in an extremely optimized campaign—like, for example, wherein at level 5 you mortgage all your gear for a candle of invocation so you can chain bind efreet for infinite wishes—, the existence of partially-charged wands likely isn't an issue.
Let me be clear here: I don't mean the presence of 1-charge wands is unbalancing in that one PC will outshine another. I mean that the presence of 1-charge wands is unbalancing in favor of the DM. They are, bluntly, too inexpensive and too easy to use.
Most of what Team Antagonist does it does off-screen. The presence of 1-charge wands in the campaign means that the DM can say that any spell that fits into a wand is currently active on any NPC who has just become obvious to the PCs.
This is a lot of brainpower to devote to each NPC, especially in the standard, high-magic Dungeons and Dragons campaign. The list of spells an NPC could have on via 1-charge wands from the core rules alone is vast, and NPCs will, if they're smart (and many are smart because the DM is not a goldfish), have already used those 1-charge wands before encountering the PCs because the PCs are dangerous, cast spells, and may also be using 1-charge wands. The presence of 1-charge wands creates a really fragile, ambush-heavy environment that emulates poorly what many consider typical heroic fantasy adventure stories.
I read what I quoted above from the Magic Item Compendium and started equipping NPCs with 1-charge wands. Team Antagonist's power stacks up incredibly fast for a tiny fraction of what's considered the normal price. A few sessions of ambushes by such foes, and I couldn't do it anymore. The PCs had seen powerful opponents with seemingly inexplicable abilities yet possessed of little treasure, and it felt like cheating even though the MIC said it was okay. The presence of 1-charge wands tilted the game unfairly in the DM's favor. Your experience, of course, would probably vary, and note that I am—shock!—prone to excessive self-analysis.
The presence of ubiquitous 1-charge wands in the campaign makes it far too easy for the DM to say things that many players hate, like The bad guy escaped but you don't know how or You don't know why your attack missed but it did.
A few used wands are fine
If, for example, a PC wants to buy a wand of knock with 6 charges or whatever, that's probably not a big deal. However, I suggest such items only be available for purchase in towns that usually carry the same full-charged item. Thus a wand of knock—whether it has 50 charges or but 1 charge—wouldn't be available in any town smaller than a large city (DMG 137), the idea being that folks who transact in wands of knock reside in such places, no matter how many charges remain in their wands. Alternatively, I suppose, in a campaign wherein thorps and hamlets are boomtowns catering to dungeon explorers, small towns might have a plethora of appropriately-priced partially-charged wands scavenged from the corpses of fallen adventurers.
Either way, partially-charged wands shouldn't be the norm, buying a wand with the exact amount of desired charges should be difficult, and make it an adventure to find, for example, a level 5 trapsmith with the feat Craft Wand before allowing the PCs to go off the usual list and buy wands of clairaudience/clairvoyance [div] (PH 209-10) (1st-level spell at caster level 1) (750 gp; 0 lbs.). Wands of spells the DM thought far beyond the PCs' reach may be within their grasp using specialized spell lists.