The "Your tweets retweeted" page on Twitter shows which of your tweets have been retweeted, but usually it says something like "retweeted by @madeuptwitteraccount and others" is there any way to find out (a) how many people have retweeted a tweet and (b) what their twitter IDs are?
The list of users that have retweeted your tweet is listed below the text you mention.
If you hover over each of the avatars it displays the users name
Twitter will always display the " and others" regardless of the number of retweets a tweet has received.
To demonstrate this, you can check the number of retweets made by using the API.
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Recently Twitter has gone a lot of changes and with the new Twitter website this is not possible. However, I use Timeline Tweets which has a feature to view all your tweets retweeted.
I hope this helps.
The answers so far will only give you at most 100 retweets. There is an API method that returns up to 100 entries of a cursored collection (so you can page through it to get more), though.
Edited to add: That said, the first thread on the Developers site that surfaced in a quick google has @episod, a Twitter employee saying: