My favorite "all around" lens is actually a camera, the SX50, which has an "equivalent" 24-1200mm lens! see
http://www.bobatkins.com/photography/digital/canon_powershot_SX50_HS_review.htmlWhile it clearly can't compete with DSLR image quality (though at ISO 100 it's not
that far behind), it's very convenient, very small and light and very flexible. Though the SX50 has gone, the SX60 is similar in concept and function, but with an even large zoom ratio (21-1365)
http://www.adorama.com/ICASX60.html?kbid=12417 I've shot with one and I liked it. It was more capable and faster than the SX50.
I've also been tempted to take a look at the Canon G3X
http://www.adorama.com/ICAG3X.html?kbid=12417 with a larger 1" sensor and a 24-600/2.8-5.6 lens it seems like it should be a pretty versatile camera. I still haven't had my hands on one though.
I've never boon a huge fan of superzooms for DSLRs. If I had to throw on one lens for general photography it would probably be my EF 24-105/4L IS USM. It's fairly fast, pretty sharp and I can use it with both APSC and Full Frame bodies.