Like:
4mm Bananas, easy to connect/disconnect, good enough current carrying capability,stackable sometimes, pretty sturdy unless you cheap out
The IEC kettle/computer/anything plug, it makes good contact, earth connects first, good insertion feel, solid
JST-XH Mini connector, good retainer, solid feel, standard 0.1" spacing! just don't get the cheap ones, which take the socket housing with the plug leaving just the pins on the board when you disconnect them.
The new apple lightning connector - the only problem is it is proprietary and has a fucking IC in the cable.
DisplayPort and MiniDisplayport - they fit solidly and don't anywhere near as bulky cables as HDMI.
Dislike:
USB connectors in general, the type A connectors should be uni directional, like the lightning connector, the micro b just isn't solid enough for repeated insertions like it is.
USB "thin" thumbsticks/drives/flash devices - usually one side is metal, so if you put it in backwards, you short your USB port, sometimes turning off the computer.
HDMI - not enough physical support for such large cables, also, you can mash a USB plug into it.
BS1363 - I find they sit too flush and make them too hard to remove from sockets, feel solid though.
"Lighter" sockets - they're old, big, don't fit well, don't carry much current, just bad all round
Almost all terminals for cylindrical batteries - you have a bunch of batteries in a holder, bump the holder and you lose connection for a moment, making the device restart!
Undecided:
DVI - while it isn't entirely clear which way it connects, its pretty damn solid for being such a big connector - i have never felt a flimsy dvi connector.
Australian Power Plug AS/NZS 3112 - I haven't ever really had any issues with it, and it's somewhat compatible with the chinese plug too, however, it can be a bit odd to plug in "blindly"
RJ45/8P8C/ethernetthingo - For new plugs and sockets, they feel solid and feel nice to insert, however the tabs can break off or act like hooks on other cables, there are plugs wiht flanges to fix this but no "diy" plugs have them.
"DC" barrel jacks - they carry current well and are easy to connect and disconnect but there are so many varieties that it is too confusing to use, also, the sockets often seem to ahve inadequate strain relief and break off the boards.
Apple Magsafe - they're good in theory for not smashing your laptop, and they're reversible, but they're proprietary, i haven't had one wear out but others have mentioned it, i can see this being an issue as with exposed contacts.
Other:
I noticed a bit of mention of RC connectors in this thread and I thought I'd chime in with opinion;
I use packs in series very often, 12S packs are ungodly expensive, so I need a connector that can join packs in series, which pretty much any "safe" connector can't do, because it requires positive to negative connection, so usually you have to use bullet style connectors, but these leave the bullets exposed when disconnected, and that is a very bad situation, my connector of choice is the XT150,
it's pretty big, and rated for 150A~, it comes in three colours (so you can use them from motor to ESC too), there are shrouds on both male and female connectors to avoid shorts but can be connected in series.
Just a pic of them:
https://dl.dropboxusercontent.com/u/677635/IMG_20130825_151357.jpg