What about gnomes or Drow, who can innately cast spells as part of their race?
Both have spell-LIKE abilities, not spells. They are not spellcasters by simply being members of their race. I suspect it is for this reason they have spell-like abilities and not spell abilities. Plus, if they were considered spellcasters (they aren't but if they were) then they would be members of which class? (They aren't so that answer is "No Class/None/Null".)
So Paladin or Ranger can use wands, even if they have no caster level.
While it doesn't mention anything under the Wand description it does say the following under Use Magic Device:
srd said:
Use a Wand
Normally, to use a wand, you must have the wand’s spell on your class spell list. This use of the skill allows you to use a wand as if you had a particular spell on your class spell list. This use of the skill also applies to other spell trigger magic items, such as staffs.
Under this condition, as far as I know, the ranger and cleric DO NOT POSSESS spell lists (yet) and thus cannot use the wand, normally

. When they get spells per day "0" they can, even if their casting stat is too low.
(Unless I've been playing the game VERY wrong for many years now.)
As written, they could also use a Scroll, based on a dice roll: You have a 5% chance of failure per Caster Level that you're short. They are the "right class", they just lack the right caster level.
It says something similar to the wand bit under UMD for scrolls too. It is an odd place to put these rules though.
srd said:
Use a Scroll
If you are casting a spell from a scroll, you have to decipher it first. Normally, to cast a spell from a scroll, you must have the scroll’s spell on your class spell list. Use Magic Device allows you to use a scroll as if you had a particular spell on your class spell list. The DC is equal to 20 + the caster level of the spell you are trying to cast from the scroll. In addition, casting a spell from a scroll requires a minimum score (10 + spell level) in the appropriate ability. If you don’t have a sufficient score in that ability, you must emulate the ability score with a separate Use Magic Device check (see above).
This use of the skill also applies to other spell completion magic items.
Also, the descriptions for both Paladin and Ranger include the phrase, "Line other spellcasters...". Not exactly definitive, but it's something.
I would assume the missing part of that sentence to be "Like* other spellcasters (who have spell lists)..." I suspect this throw away line is less important than the actual parts of the rules that say what happens and the official rulings from WotC (or their reps). But once again, I might be wrong as far as the official rules go. I don't have the original source that I'm referencing, it is entirely from memory. I wouldn't even know where to start looking for it - I don't remember the details, just the ruling.
*I'm assuming it was "Like" and not "Line"
Quick question Greenfield. Why do you start posts like this? With questions that either have no answer, or are purposefully working on the fringes of the game? This is CharOps level readings of the rules most of the time and I've got to wonder why it matters? Most of the time you seem to have your own interpretation and I doubt this is for your own personal character, I'm guessing you are the DM anyway and so why not just go with whatever makes the most sense?
I mean it has always bugged me that scrolls and wands and what not are based on the class that the spell is from. I'd rather go with a source - so paladins, rangers, druids, clerics, etc. can all use divine scrolls/wands; and all arcane classes can use arcane scrolls and wands. This has never really come up but I probably would rule that way, regardless what the official rules say.