I just finished the civil war and fasty travelled to Dragonreach. When I entered Dragonreach, Hadvar was there behind me, sword drawn. I can't talk to him and can't seem to get rid of him/ Any suggestions?

bug. also had it for a while. he will dissapear after a while. you will have to live with him till he leaves. staying away from whiterun for a while could help.

It's a bug. It happened to me, too; what I did was follow the advice on the Elder Scrolls wiki. Quoting the wiki, '

• Solution for the above bug is to get as close to him as possible, save the game, exit to the dashboard/xmb/desktop, and load the game back up. He should put his sword away and walk out of Whiterun. (Confirmed on Xbox, PS3 and PC, both patched and unpatched versions). Sometimes this might not work, if you wait a couple in game days Hadvar will leave you and go to the inn in Riverwood.'

It worked for me when the bug happened, so hopefully it'll work for you, too.

I was also having this problem with him following me all over Whiterun, but I just left Whiterun for awhile to do other quests, and eventually it stopped. Im not sure if a certain quest triggered the fix or if over time he went away on his own.

If he's still around, ask him why he hasn't reported to general Tullius in Solitude and secured your pardon. I mean, by the time I got there, Tullius didn't even know that Hadvar had survived Helgen! I think Hadvar is a deserter, and possibly a skooma-head.