I'd find it strange and something they should grow out of.I don't have GSD's though. I like Antony 8858's reply to train them to wait for you when you wish. I'd say it is some sort of mild separation anxiety to need to follow you around everywhere.
I disagree (not with Anthony's suggestion, but with the separation anxiety bit). My dogs do not demonstrate anything even close to separation anxiety. The only thing that might fall into that category is Hector being clingy for a day or two after I'm gone for a weekend, but he's fine with the pet sitter and I can leave for hours right after I get back and he's fine, and his body language isn't anxious despite his desire to be right with me more than usual, so I don't think it counts.
I am not sure what breed you own obviously, but wanting to be very close to their owners is a trait that is bred into some dogs. Both my breeds (ACDs and GSDs) are that way. It's especially common in herding and guardian breeds--they wouldn't be much use if they didn't care where their "charges" were! Hector is actually funny because if I'm in the bedroom and my boyfriend is in the living room (or vice versa), Hector will often station himself alone on the bed in the guest room where he can keep an eye on the hallway that leads to both rooms. Either that, or he'll pick one of us to hang out with (generally whoever has the most room for him on comfy couches/beds) and will get up every hour or so to do a quick check on the other person before going back. It's about keeping an eye on things, not separation anxiety.
GSDs were selectively bred in part for their devotion to their owners, so it's to be expected that it manifests as the dog wanting to be with you as much as possible. I'd only worry if the dog was freaking out when the bathroom door was closed or something of that nature.
Courtney posted: I can appreciate your post. I heard the number one reason adults end up in the ER with broken bones is from tripping over a pet!
LOL I routinely have 4 dogs following me everywhere I go, but I have to say, my cat is the real threat! I swear that little sucker enjoys lurking in darkened hallways (and he's black so it's not like I can see him easily) and then darting out under my feet!