Critics lump this sonnet with others that Shakespeare probably wrote to a young man who was his patron and probably lover.  It is inevitable that some find sexual entendres in the words “love’s loving parts” (3) reflected again in “all their parts of me to thee did give” (12).  We tend to bury this suggestion because of the tone of the remainder of the poem (which mentions “dear religious love” and “ holy and obsequious tears,” and “ the grave of buried love”), finding it sacrilegious to bring such matters of bodily parts into the sanctity of the temple. Perhaps there is a suggestion which deliberately undermines the seriousness of the sonnet, implying that “You have indeed all my love, all love past and present, and all parts of it besides, so beware, for you might not know what all those parts really are, and you might get more than you bargained for.”

Brendawn's line by line analysis is excellent. I'd add a slightly different interpretation.

I find more hope and renewal than disappointment and bitterness here. My reading hinges on several points. First, he says he has found all Love, everything he thought was lost or dead to him, in the bosom of the person he writes this poem to. He has found a lover with a capital "L", and his connection with the person has allowed him to reconnect with all of the love he has felt in the past. He says he finds (in her) that which he "[lacked] and have supposed dead"; because he lacked those feelings, he thought they were dead to him or gone forever, but that does not mean that they are gone now. He finds that although he cried as if he had lost all love, it now appears that it was not gone, but that it was merely removed and hidden within her(4-8). The next part is the section that makes many read this poem as bitter--his metaphor is that she is a grave, a keeper of dead love, all of his dead loves. Here's where my reading diverges:

He does not say that she kills love or destroys it, but that it lives within her. Consequently, though he uses a metaphor of death, death functions to remind us of life. He thought he could never love again; he thought all love he felt in the past was dead and buried. However, if they were buried, they were buried within her. Now whatever love he would have given to others he can only give to her, and he gives her his all.

This is a line by line translation: 

You have the love of everyone who used to love me, people who I supposed were dead because I didn't have their love anymore. Love reigns in your heart—both everything belonging to love and all those friends who I thought were dead and buried. How many tears of devoted love have I shed at funerals, in payment to the dead, when now it appears they had only gone to hide in your heart. You're like a grave where dead lovers come alive again, decorated with mementos of those lost loves who gave you all the love I owed to each of them. All the love I owed to many is now yours alone. I see these lovers in you, and you, who contain everyone I have ever loved or was loved by, have all of me.

This is a reflection on love, communicating bitterness and disappointment, while suggesting a lack of recognition and appreciation on the part of the beloved.