Welcome to PT Andrea...Yes there are lots of similarities!
Lots of characters and themes are very similar. I have just gotten into Tolkien rather recently and just finished LOTR myself, maybe your experience was different. I actually kicked off my fantasy reading with HP and it was a thrilling introduction to the genre. Actually I'm glad that I did it that way because only after I read LOTR, did I understand how much Rowling borrowed from the fantasy warehouse of ideas, and if I had known I probably would not have enjoyed it so much. I do love HP and I am waiting for the fifth book just like everyone else. It has plenty to offer in its own right but like I will probably say forever now, it ain't LOTR...I actually think I'm pretty much done with other fantasy fiction postAuthorIDs now that I have read it because it probably doesn't have a chance to measure up!
Particular similarities I have noticed are the characters of Gandalf and Dumbledore, Sauron and Voldemort, and Frodo and Harry...plus the birds who became impromtu charter planes in each story, hahaha...
I started a thread to compare/contrast Tolkien with CS Lewis if you are interested? Specifically Middle Earth and Narnia. And there is a thread called The Return of Exactly What are You Reading Right Now? Plus if I remember correctly, there might be a thread or two about Harry Potter....check the pubs! I hope you have fun here, it's a place for both fun and information!