How much is winning initiative worth?
In 4th Edition, your initiative is the result of a d20 roll, plus half your level, plus your dexterity modifier. Higher numbers act earlier in each round than lower numbers. You only make one roll per combat, which persists across subsequent rounds.
In previous editions, there were a host of very powerful abilities, from Sleep through to Power Word: Kill, which could substantially alter the battlefield, if only you could cast them before the enemy acted. In 4th Edition, everyone has more hit points, and "save vs death" effects are gone, so the chances of a first-round kill are substantially less.
I've heard it said that acting before the monsters is like getting an extra turn in combat that you otherwise wouldn't. That's a fair way of looking at it, and an extra turn in 4th Edition is a very valuable commodity indeed.
There is also the luxury of being able to delay your action; you may, on your initiative, choose to not act until some later point in the round. If you have not used your action by the end of the round, it is forfeited. Once you take the action, your initiative for the rest of the combat is set to whatever point in the initiative queue you ended up actually acting. This option is therefore much more useful when you start with a good initiative result.
In addition, on the first round of combat, and the first round only, Rogues gain combat advantage against any enemies that they beat at initiative. This is usually the difference between them being able to backstab for 2d6 (or 2d8) additional damage, and not.
It's probably fair to say that, for non-Rogues, beating the enemy at initiative is worth, on average, about 1[W] damage (the base damage of your weapon) per combat in the Heroic Tier. That's taking account of the possibility of misses and suchlike. Let's call it 1d8 damage. So what does it cost to win initiative?
Firstly, it's worth noting that initiative is keyed off the Dexterity stat only. By contrast, the four defence values are each keyed to the best of a pair of statistics. AC takes your best of Dexterity and Intelligence, for example. Fortitude takes Strength or Constitution. When Initiative breaks the mold, it's telling you that it specifically doesn't want to give a high initiative to casters, who would have benefited from the Dex / Int pairing - only to strikers, the Dex side of the equation.
Why not to casters? While save vs death effects may be gone, casters are still in possession of vicious AoE damage and debuffs. Giving enemies the chance to scramble for cover before getting nuked makes for a more interesting game - one where the presence of a caster doesn't automatically result in the other side getting debuffed in the first round. The Dexterity focus also adds more flavour to the strikers. Seeing Rogues and Rangers act before anyone else becomes part of what makes their class distinctive.
To buy a better initiative than your Dexterity would other permit requires feats. Improved Initiative adds 4 to your initiative. It's not coincidence that that's the same bonus you'd get from an 18 or 19 in Dexterity. The feat is, effectively, letting you be treated as a striker for the purpose of initiative.
Improved Initiative should be enough to let you act before same-level enemies about 50% of the time. So, 1d8 once per combat in every second combat. That's two extra damage per combat, on average. It's probably worth a little extra because it's giving you options, as well as damage.
Compare to Weapon Focus, which gives +1 on damage whenever you hit with your chosen weapon group - which should really translate to "whenever you hit". How often do you land an attack in a typical battle? Two or three times? So that's... a little over two damage per combat?
It seems balanced. Note, however, that I was working on averages in regard to initiative. This is the bonus you get if you enter combat with an attack that deals 1[W] + stat damage. If your average damage is significantly larger, but you're not already winning initiative - that is, if you're a warlock, or a damage-focused fighter, or suchlike - then your benefit from moving up the initiative queue is significantly higher.
Note also that Improved Initiative continues to deliver a high value beyond the Heroic Tier. While adding half your level to initiative means that a +4 bonus becomes a progressively smaller part of your initiative total, it still scales much better than Weapon Focus' +1 damage, which becomes comparitively useless beyond about level 5.
Improved Initiative is one of the more valuable feats in the Player's Handbook, and if you're focused on maximising your damage it's an option that merits some serious consideration.