Dragging a ship from your ship hangar onto the 3d ship view part of your screen will cause the ship to become active.

You can customise your left/right hand tab (NeoCom) by rightclicking on it and removing/adding icons to it, as well as making it behave differently (autohide/iconzoom).

You can merge your ships and items tabs into the station interface through the Generic options menu (Esc).

Dragging a whole lot of modules (selected with ctrl+A or shift + click / Shift + ctrl + click) onto the fitting screen will put them in order in the empty slots you have. NB: The above still doesn't work properly with ammo though (puts 1 unit of ammo into the first slot :( )

Dragging an item onto the ship's icon in the hangar will put the item in its cargo bay.

You don't need to open the cargohold to put stuff into it in space - drag it onto the little cargohold icon instead.

You can split stacks by shift-dragging and in some cases by right clicking and selecting 'split strack'.

You can 'top up' containers by dragging excess amount of items into them and accepting the dialog box regarding volume.

You can use various sized containers (not only secure) to increase your cargohold total. Note that this will not work with bio matter and some radioactive / special items and other containers, as well as can prove impossible if you want to transport bulky items. The containers give you 30% extra space regardless of their size (i.e. 3000m3 can provides 3900 m3 space).

Hot-firing 2 tractor beams will activate them on the target but will not give you any benefit whatsoever ;-)

Salvaging is (as of now) not theft. Looting cans - is.

You can select multiple items with the same set of actions (e.g. containers) and perform the action to all of them. Be it "Open container x10", "Repackage x16384267" or reprocess commands. Save for reprocessing, it is safe to select 10 containers and a few exotic dancers and still select open container (10). The dancers will just ignore you while you increased the speed of your hangar sorting operations ;-)

You can right click any cargohold or hangar and as long as there is enoough space to do so, you can 'stack all' items that are repackaged. (Yes, I've seen ppl do it manually on their whole hangars).

You can check any standings towards you in your character sheet. If you are looking for a new agent - see which corp has best standings towards you, 'info' it and see what agents they offer. Alternatively you can use the map, but prepare to spend the rest of the day looking for the one you want if your standings are quite high ;-)

You can speed up system search by looking for it through ppl&places rather than the map search function.

You can make your map skip the animation by selecting the 'instant' option in the animation tab.

You can access your map by doing ctrl + mouse scroll back (and conversely - forth).

Read and customise your shortcuts menu (ESC -> shortcuts) in order to avoid dissappointment like all chat windows disappearing (default 'ctrl+shift/alt + W' if i recall correctly) or game suddenly shutting down (ctrl+Q by default). You are also bound to find a lot of cool shortcuts like autopilot switch for instance.

During missions/plexes, only shoot structures with a wanted structure icon (a spiky square) rather than a plain square, if you don't want to drop your standings for no reason whatsoever.

Read and re-read the item descriptions - EVE is constantly changing and that old nanophoon of yours might want to get some istabs instead, etc.

It is useful to read patchnotes if you don't want to spend hours figuring out things like why thi time your control tower lets you top up for 21.5 days. \o/

I shall come back with some more later if I can think of something not mentioned here (though I'm pretty sure I doubled up some tips already ;-) )