Aye, it generally depends what you are using the monitor for
Display port (DP)- The main reason to use this is if you want to run eyefinity as having a Display Port connection is very useful as you don't need to buy an active adapter (also you can use a DP1.2 hub to connect to multiple DP1.2 monitors from a single Display port graphics output. Also if you have a professional grade monitor and graphics card you can use a DP connection to make use of higher colour depths.
HDMI - the main reason to use this over DVI is for the carrying sound signals (DVI doesn't carry sound). So if you are connecting to a AV Amp or your main audio device runs off your monitor/TV then HDMI is preferable. Also, if you want to run 3D content to a 3DTV then a HDMI 1.4 connection is pretty much the only way available at the moment.
DVI - I would recommend this be your default connection type unless you need the special features mentioned above. With DVI you usually don't get an hassle with overscan/underscan on monitors and the image quality is just as good as the above connections. Also, dual-link DVI has more bandwidth than a HDMI so with this connection you can run very high resolution monitors (2560x1600@60Hz) and drive a 1920x1200 monitor at 120Hz. Also, using 120Hz monitors is how current 3D PC gaming system work - making use of a dual-link DVI connection.