[realbeerguy]

Store upright or on side keeping cork wet?

[chezteth]

I would say store on the side just like wine.

[jaybeerman]

do you want cork flavor? are you using real cork? how long will you be storing the mead? 

[realbeerguy]

Using real corks.  Looking to cellar some for 2-5 years.

[tumarkin]

I'd highly suggest leaving them upright. Good quality cork will keep a good, tight seal for longer than that without drying out. You don't want to risk cork taint (off flavor) from contact with the cork. You might want to dip the cork & top of the bottle in melted wax. It gives a nice look (presentation is a plus) and will provide additional protection to the cork.

[The Professor]

After having some corks dry out on early batches, I have since then always stored mine on their sides and have perhaps been lucky not to have cork 'taint'. 
In any case, these days, I am using the new plastic corks which are superior to natural corks.  I also use screw top wine bottles when I can get them.  They are the ideal and most sensible closure for wine anyway.  It's nice to see some high quality wines in the stores these days sporting the handy screw tops.

[jaybeerman]

I agree with Tumarkin.  No need to lay them down.  I've always used the champagne corks with a thin layer of real cork on the bottom, the rest is a composite.  No issues thus far.