Our garden is home to quite a wide variety of garden birds plus a few unexpected woodland and countryside birds. However, I always feel I can attract more. I put out a wide variety of food too, which helps. Goldfinches were a species which didn't used to visit our garden until a couple of years ago. While these birds are very common, quite tame and easy to see and hear, they are very fussy eaters as far as seeds go. We used to just feed whole black sunflower seeds and peanuts. At this point we had not seen or heard Goldfinches in our garden. It was only when we started to feed nyjer seeds and sunflower hearts that the Goldfinches came. At the time seeing the first Goldfinch in our garden was very exciting but now they are just as common as other birds and we take the presence for granted. I would like to get the same exciting feeling by attracting other birds, but I need help! The pictures below show a juvenile Goldfinch seen in our garden recently:
So, what are the birds that I aim to attract to my garden. Well, some of the less common and occasional visitors are: Bullfinches, Great Spotted Woodpeckers, Wrens, Goldcrests, Jays, Bramblings, Song Thrushes and Mistle Thrushes. These birds are all breif visitors, but I would like to attract some other birds too. One of the most common birds that has not been seen in my garden is the Nuthatch. Now I know for sure that a lot of people reading this will have seen one in their garden. I have seen one on holiday, but never at home.
These are colourful, small and acrobatic birds that I am sure are very entertaining to watch. But I am not sure how to attract them. I already put out peanuts, seeds of various types and fats. Does anybody know what else I could try feeding to attract them? The image below is from wikipedia. This must be a pet Nuthatch! 
Another wanted bird in the garden is the Pied Wagtail. I have seen this bird countless times in car parks scavenging on food, but surprisingly this bird is not quite so common in gardens hence why I have never seen one. Not a particulary thrilling bird to watch, but important to feed nonetheless. I'm not sure if there is anything in particular that will attract these birds, but please comment if you can think of something. As far as I am aware they will not nest in nestboxes so I am not sure if there is an awful lot I can do for this bird. The picture below is again from wikipedia.
In fact this bird is probably one of the only ones that benefits from human activity, so it is maybe not essential that I feed these birds specifically apart from just to experience seeing it.
The Tree Sparrow is the bird I would like to see the most. Its close relative, the House Sparrow is recognised by birdwatchers all over the world, but the Tree Sparrow is a seemingly declining species. Its habitat is more in the countryside but is sometimes spotted in gardens too. I think its a real shame that this bird is struggling because it is one that would be fantastic to see alongside its common relative. It is more neat and tidy looking than the House Sparrow as shown in the photo on wikipedia. I have never even seen this bird even outside my garden so it is difficult to picture what the bird would act like. 
The last bird on my list is not actually one bird. But it might as well be because it is often impossible to tell the two birds apart. They are the Marsh and Willow Tit. Again, I have never seen one of these properly in the wild, but I think I may have seen glimpses. They are a lot shyer than the more common Tits so it is not surprising that I have never seen one of these in my garden. While there is woodland near our house, their main habitat is probably more dense woodland.
I am guessing that if they visited feeding stations at all, they would take seeds but please correct me if I am wrong. This is probably one of those birds that has visited our garden before but hasn't been seen. It was very sad to hear that the numbers of Marsh Tits has decreased significantly over recent years. On wikipedia it says, "There has been a >60% decline in numbers in Britain between 1960 and 2000, with numbers down to 52,800 pairs". Now I know why I am unlikely to see them!

Now I have written all this I realise that my list is quite ambitious. If I don't see these birds in my garden (which is highly likely), I will hope to see them more when I am out elsewhere.
First 2 images were taken in my garden on 28-09-08. All others are from wikipedia.