It depends on the situation, but generally, the answer is even if you could it possibly won't be worth while.
You can though, (at least on a desktop PC), type when most combo box is expaneded/selected to find a value... If you visit the DHL site you will see a drop down list. Click the list to see the options and whilst it's open type United K
(including the space) and you'll see it will jump to the item.
Some drop down lists won't allow it, such as this site... The most likely technology used would be JavaScript so may be a GreaseMonkey script could help to turn off the behaviour so it acts it's standard HTML way.
Things like Greasemonkey will allow you to affect the rendered HTML and possibly convert it from a combox box to a search box, but, the thing about a combo box is it's predictable! We know what options we have and therefore, what can be selected. We don't typically code against unexpected value errors since there isn't likely to be any! This may mean by typing in words which don't exist could result in unexpected behaviour.
With web apps, it's potentially more complicated as other technologies can be used...
And of course, each browser may react differently too, so in conclusion it's not really possible to answer, but my answer is no, you can't do what you want without error (or at least, working exactly how you want) for every webpage!
As discussed in the below comments, the Greasemonkey solution is the way and it will never(!) (wink wink to Dave and random) become outdated until browser-level and/or OS-level software will make all combo (aka select, aka drop down) inputs as searchable as de facto standard -- which is completely doable and I can bet on it that it will eventually happen (just like the passwords inputs are nowdays getting special handling at OS and browser levels). – Alex – 2014-10-02T05:10:51.927