I personally bring my two 600-watt Harbinger 15" powered speakers. The nice thing about powered speakers is that even if one did fail, you can get by with just one in most cases (as opposed to a stereo amp that fails completely). I have never used a powered mixer. I use a Behringer EuroRack 1604 mixer (bought in 2002, self-repaired it a couple times since), and I have a smaller backup mixer just in case (both use same 18VAC power supply/plug so there's always a spare of that as well).
I do also bring an amp and one 15" speaker that I face into a corner behind me, with a homemade inline crossover, used as a subwoofer... really adds a lot of oomph to the sound... but that's extra and I don't always break it out (depends on the room, and doesn't do much in an outdoor setting).
Since the two main speakers are powered, I just always have as many extra IEC power cords, and XLR cables as possible, along with a bunch of 1/4" cables. Extra mics (two wireless, plus 4 wired "Justin Case" mics, one of which I use with a mini desk tripod stand).
I have a large Rubbermaid tote, with several grocery bags inside. One bag is nothing but XLR cables, one power cords, one HDMI, one RCA, and one 1/4". They are color coded (yellow = Dollar General, Beige = grocery store, and so on). So if a cable is bad, I can very quickly find a swap-out, and set aside the bad one for later inspection, repair, or replacement... (some of my XLR are homemade so I don't mind replacing a connector or whatever later on).
In another tote, just extension cords and power strips of all sizes/lengths.
Final tote - mixer, mics, wireless mic receiver, and misc. tools and such (screwdriver, pliers, elec. tape, etc). As long as I have my three totes, I know I have extra everything.
My lights are in a milk crate, as they just fit perfectly (I got rid of all my heavy halogens and I'm all LED now).
I do always bring an extra laptop (2 in one bag), extra USB sound card, and of course in a pinch I can play Pandora off my phone (say Windows is acting up and needs rebooting, Pandora will buy a few minutes without dead air).
Because I never know what situation I may be walking into, having extra cables of every type is a must. You might be very far from the nearest electrical outlet, or you may need to run speaker cable a long distance or over/around obstacles (like over a doorway). With the XLR you can just chain as many together as you need, and locate the speakers near outlets of their own.
One final note: a wiring tester is a MUST. If you are in an older building where perhaps someone put 3-prong outlets where there were only 2 before, and one outlet is wired in reverse -- let's just say I smoked a mixer because some equipment was on one outlet, and some on a mis-wired outlet. Once you connect the audio cables, you've got ~115 volts flowing through the cable shield... a $3 tester can prevent that expensive mistake (luckily I was helping a friend and it was his mixer... and the venue reimbursed him for a new one).
<shameless plug>
There is a book covering all of this and more:
http://www.vdj.net/howtodjbook.php</shameless plug>

I plan to update the book soon, and put it online for free (don't tell everyone that yet though

)... after the next VDJ is released. I'll probably make more money having a small ad on each page, than trying to sell dead-tree books in the 21st century lol... plus it can be updated more easily, it'll be like a live always current book.