The most irksome thing about my work during my recent vacation was lugging my laptop everywhere. Apparently I banged it against something and now Dell is busy fixing it for me for $500. Grr. But other than that, it certainly wasn't preventing us from having a nice time.
Also, there are a lot of activities which aren't as critical as you think they are. I was used to doing bug fixes the day they were reported. That's nice, but that's not a law of nature, and you probably don't want to make your customers think it will always happen. If someone reports a bug during vacation and it isn't killing someone or taking the site down just tell them "Thank you. I'll see to it after I get back from vacation."
For me, the new definition of a vacation is being completely unplugged. Granted I don't have my own business yet, so presumably daily check-ins are OK/necessary - but even then I'm not sure I could properly 'disconnect' and relax.
It worries me that even for relatively low-level staff it's not uncommon to get email responses when they're "on vacation" nowadays.
Your goal should be to minimize your customer support requirements. For the past two years I've treated every customer inquiry to my business as a bug requiring a fix.
If someone asks me for additional information about a product, I add a section to that product's description page or, alternatively, make the existing content clearer. If someone has trouble with a download, I improve the instructions sent with my payment confirmation email and perhaps increase the font size of the most critical links in the admin area. In-line instructions, such as those used by the 37 signals team, help greatly in this respect.
Over time this has worked and customer support requirements have dwindled, and with less emails to answer per day you can afford to be away from a machine for longer.
Actually my problem was that I found myself working on many issues that were scheduled after vacation. Body was on vacation, mind wasn't.