Is there a website with an up-to-date worldwide list of cell phone carriers searchable by phone number?
Wikipedia has some pretty extensive lists of mobile network operators :
This answers your the first part of your question - as for the second - searchable by phone number, is going to be tricky. You've not said if you just want to lookup numbers yourself or are trying to write / integrate the feature into some sort of application.
For the former, There seem to be a lot of web sites offering country specific lookups, but none/few offering global searches. The latter, integrating it into your site / app, a quick Google brings up Mobile Network Lookup, this looks like a good starting point, but I'm not sure how reliable this is.
One word of warning about relying on "static" lists of data - e.g numbers 1234-0001 to 1234-4999 was assigned to Operator X. Certainly in the UK, and most of Europe, it is quite common to "port" your number to a new operator when changing contract/subscription plans. This makes such static lists obsolete quite quickly