I'd like a slight twist on @
Kzach 's proposal: Higher level characters shouldn't have MORE options, but BETTER options. If characters get lots and lots of options, it leads to slowdown at the table as players sort through all of their options and try to decide which one to use. Swapping out a low-level option for a higher-level option would be fine by me, though.
Get a good grip on the full range and scope of options before you release the game, and you can finesse this issue: Make it so that those higher level options are expanding the scope of what the earlier option can do. Of course, if you are going to do that, you might decide to build such "horizontal scaling" into the options from the beginning instead of replacing them.
This pretty much kills feats as we currently know them--or radically changes them, if you want to call the new thing "feats." For example, let's say that a martial character has the option to get better at disarming, over whatever the basic "moderately real-world-like, only works in some fairly narrow situations, when used unexpectedly," version of disarm is. Say that the base version is limited to one-on-one duals with characters of about your size, and no more than one attempt per fight. The first level character picks the "improved disarm" option, and can now try it against characters one size larger. As the character levels, the percentage chance to disarm doesn't move much (beyond whatever the standard, slight attack bonus scaling does for you). But by max level, the character can pretty much attempt a disarm against anyone, any time, if they are holding something in their hands.
Similar things can be done with spells. I believe several people have suggested such options as ways to have spells scale without having to do slightly better versions every few levels. However, an even better effect of such a system is that it gives you flexibility in how widespread your improvements are. Let's say that there are options for casters to become masters of fire or lightning of shaping effects. The fire master gets to do all kinds of neat things with his fire spells, including having them wrap around friends to hit enemies. But he can also ramp up the area, range, etc. The lightning master can do some similar things (i.e. some overlap with fire, but not exact). Whereas the shaping master can't do all that other stuff, but he can shape his fire, lightning, acid, cold however he wants.
One of the problems with such abilities as discrete feats (e.g. "enlarge spell", "improved disarm") is that they build off of other bonuses, and when stacked in certain combinations produce the overpowered characters--or don't stack so hot and produce an underpowered character. Contrawise, if the ability is a major package with a gradually unlocking scope (in a system as discussed in this topic), then there is not much effective stacking.