Ok, so I've got this strange thing going on - not sure where to start looking.

I've got something like a mixture of some grease with some oil at the bottom of the bike - around where the kick stand is hooked to the bike and under the engine and a bit on the side - basically the very bottom part of the bike. There's also a bit of an oil-like stain under the very front of the engine when it's been parked for a while - but I haven't seen anything dripping down.  Finally, there seems to be some sort of wetness over the top of the engine.

I'm not sure where it's coming from - as everything seems to be in place.  Engine oil level is fine, forks oil is fine, chain grease is fine.  If I wipe that stuff off the bike - it's back by the time I make a round trip to work and back home. It doesn't seem to be affecting bike performance - apart from being very annoying, as it gets on my riding gear and my hands - and wouldn't come off with soap - only using solvents (I use white spirit  - works a charm).

What could it be and what can I do about it?

I think this is quite common...I've got it too and haven't identified the source of the leak yet.

At least I'm not alone in this.  BTW, mine is 97 GS500E.

What's especially annoying is that I have a nice Oxford soft nylon cover, which fastens underneeth the bike.  The fasterner is now all covered in this stuff - and I can't get it off it - basically ensuring that I have to wash my hands in solvent every time I take the cover off.  I stopped using the fastener - and just hope the wind wouldn't blow the cover off

Ha, I posted a very similar question years ago, Kerry had a funny & helpful reply (http://gstwins.com/gsboard/index.php?topic=8754.0).  Pull the drive chain sproket cover on the left side of the bike - all kinds of grime, grit, grease, etc gets caught up in there and leaks down the kickstand & shift lever.  This is the cause of the greasy top of left foot a lot of us experience. 
Not sure this helps with your oil on the top & front  but this is a worthwhile cleaning effort.

jeff

The top of the engine thing sounds a little different.  I would carefully inspect the valve cover gasket and the tachometer cable where it enters the engine.

The oil near the kickstand is what I have.  I don't think it's from built-up grime because I've cleaned under the sprocket cover attempting to find the source.

Ok, cleaning behind the sprocket cover would probably be my first task - if I can at least get rid of teh grimy-greasy stuff, that would already be a major plus.

As for the leaking oil - if it were engine oil, I would probably see lower oil level in the engine (on the dip stick).  Yet, the oil level is fine.  I had the oil changed about 2 months ago (about 1700 miles since then) - and the oil level is still perfectly fine.

Ok, I finally got the time yesterday to work on it.  It took me over an hour just to get the gear shift lever off - it was just stuck.  Cleaned what must have been like 2 kilos of very gross and disgusting stuff - then spent another half an hour cleaning my hands (I did use rubber gloves - but that still didn't help completely).  No grease on the kick stand this morning - great!

I think I found the source of the leak too, but now I need another free weekend to look into it.  It may be the head gusket, maybe not, but it's somewhere at the top.  I'll see if I can take pictures and post them here for some advice, too.