My DD is just beginning to read independently and I want to introduce her some books/ series that will engross her. Most of the beginning reader books I have seen are too focussed on the mechanics of spelling/ reading as opposed to just a great story that you lose yourself into. Any recommendations?

the 'Usborne beginning reader' series are really good. Also DK readers are very nice too. Not sure if you have looked at these.

Depends just what level she's at (I have the impression that some children first read "independently" at much higher levels of decoding competence than others!), but for really easy stuff I'd recommend the Oxford Reading Tree Songbird Phonics. They are written for decoding, but (mostly?) by Julia Donaldson of Gruffalo fame, and there are some that DS5 still goes back to sometimes. If your DD is a bit further on than that, one thing that sticks in my mind is the set of Quentin Blake books we have - Cockatoos, Mrs Armitage books etc. Engaging words and funny pictures. Or the original Thomas the Tank Engine stories - we have a large book of all of them and probably that's what DS taught himself to read from, actually! Or if you're looking for chapter books (that kind of independently) he enjoyed the Worst Witch stories early on, or Winnie the Pooh, or... oh, it really depends on her interests, I could go on but it would be kind of random...

Thomas is a really nice level for a bit above 'beginning' but not too far. We had a book club thing where we'd get a new double book or two each month. Ds loved them, although I mostly read to him at that point. Now the set is at a cousins house being fully loved. My son sort of leapt from not reading to reading a couple of easy readers to reading captain underpants to beyond that (maybe because of a lack of compelling material at that level) - I can't think of much either!!
But we have another kiddo approaching reading so this would be great info to have. Actually, come to think of it, some of the Olivia picture books are very very enjoyable and suspenseful for short books with very fun illustrations. We have Olivia helps with Christmas, Olivia's best toy and Olivia. Our dd is not up to those, but your dd might really dig them. (so to my sluggish morning-brain, take that! )
Also, Rosemary Wells, more great illustrations, some really good writing, actually. See 'Bunny Planet'. Hope these aren't too 'babyish' for her. I enjoy them anyway

I am re-reading your post to see you said 'independently'...you might want to check out 'Frannie K. Stein, Little Girl Mad Scientist', a series. Still not entirely sure what level you are shooting at...

Have you tried some of the "adapted" books. There are many classics that have been abridged for early readers. They essentially turn each chapter or story line into its own book and adjust the language for early readers. Try the Little House series, Fancy Nancy, Charlotte's Web, Amelia Bedelia and Arthur.

If she is very, very new to reading, try the Monkey books by David Martin. DS especially liked Monkey Eats Worms and Monkey Trouble. Also (a little higher level than Monkey), any of the Dr. Seuss books, or the ones by P.D. Eastman (Big Dog Little Dog, Are You My Mother?). And later on, or now if she's ready, the Frog and Toad books by Arnold Lobel -- DS5 still loves those.

..and Little Bear.

Can you tell us what books she reads comfortably by herself? If she's ready for reading more words on a page, that opens up a lot more. My DS5, who can read at a very high level if he wants to, is just now starting to read independently. His favorite books right now are the DK readers with Star Wars stories. He loves Star Wars, and he likes that there's an index in the back of the books so he can look up whatever he wants to read about. Levels 1 and 2 are great for beginning independent readers; they run 32 pages with lots of pictures and about 3 short sentences per page in level 1, and 4-5 longer sentences in level 2. Level 3 has a couple paragraphs per page and fewer pictures. They have many themes in the DK readers, so there's a good chance your DD will find something she likes. DS liked books about scooby doo for awhile, and there seems to be no shortage of books related to kids shows (for better or worse), and they're all beginning readers.

I second a lot of the other recommendations too. Dr. Seuss is great for beginners, because they're silly and easy to read. Frog and Toad was DS's favorite when he first learned to read.

I'll go track down the threads that discuss the books that are a little more advanced...

http://giftedissues.davidsongifted.org/BB/ubbthreads.php/topics/33477/Picking_the_right_books.html

http://giftedissues.davidsongifted.org/B...tions_plea.html

When DS4 started reading on his own he enjoyed Dr. Seuss, frog and toad, Mr. Putter and Tabby, Amanda Pig and Oliver, Henry and Mudge, Little Bear. Those are nice because there are series of the books. We would try one and then if he enjoyed we could go back and get lots of the others. He still enjoys some of them from time to time because they are good little stories. Also, although they are a little overdone at times, the "If you give a mouse a cookie" books by Laura Numeroff (pig a pancake, moose a muffin, etc.). Those are all pretty good, cute stories and pictures and fairly easy to read.

My son discovered “The Time Warp Trio” and “The Secrets of Droon” series a little too late. He enjoyed them anyway, but they would have been prefect for him earlier as he really disliked the “sedate” story lines of many early readers.