The correct way to look at something is, "What kind of item is it?"
For purposes of this discussion, there's three kinds of items: Spell Trigger, Spell Completion, and Other.
Scrolls are one example of Spell Completion items (and are, in fact, the only example in the main D&D books). In order to use a spell completion item, you must have the spell on your class spell list
and be at least the caster level of the item in order to use it safely. If you do not meet the minimum CL, you'll need to make a CL check to activate it. Furthermore, at least as far as scrolls are concerned, you must be the correct type of caster, either arcane or divine.
For instance, take a CL 1 scroll of Cure Light Wounds, Divine. This scroll may be used by any cleric or druid, and by any paladin or ranger of 4th-level or higher. Anyone else wishing to use it must make a Use Magic Device check in order to do so.
Similarly, take a CL 1 scroll of Cure Light Wounds, Arcane. This scroll may be used by any bard. Anyone else wishing to use it must make a UMD check in order to do so.
The next set of items is Spell Trigger items - like wands and staves. Spell Trigger items may be used by anyone who has the spell contained on his or her class spell list - even if he or she lacks the ability to cast that particular spell yet. Spell Trigger items are neither arcane nor divine, and are useable by anyone.
For instance, take a Wand of Cure Light Wounds (the infamous healy-stick). It may be used without fail by any cleric, druid, bard, paladin, or ranger of any level.
"Everything else" - rods, magic swords, etc. - will vary depending upon the particular item, but the general rule is that anyone can use them.
EDIT: Oh, the 3.5 SRD on this subject can be found here:
http://www.wizards.com/d20/files/v35/MagicItemsI.rtf