ThinkPad laptops have a special place in my heart. My first laptop was a ThinkPad T30, courtesy of RPI. Since then I have owned quite a number of ThinkPads, and nothing but ThinkPads laptop-wise. Here are the reasons why ThinkPads are awesome.
This largely applies to days gone by rather than the current lineup, unfortunately. My T30 had a 1400x1050 resolution in a 14" diagonal. This is impressive even today. At the same time you could get an A30 with 1600x1200 resolution in a 15" diagonal. I had that resolution on a 21" CRT at the time and was pretty proud of myself.
T60 generation repeated 1600x1200 15" screens in some T60p models which unfortunately were very rare. I don't think I have ever seen one sale on the used market. Even more impressive, and actually obtainable, was a 1920x1200 15" configuration. This is a resolution found in better 24" monitors. I had such a machine and it was beyond impressive.
Smaller ThinkPads, namely X40 and X60, had pathetic 1024x768 12" screens. There were some X60t tablets at 1400x1050 but I have no personal experience with one. Tablets by their nature are bulkier than laptops and I did not want the larger dimensions.
X200 series redeemed small ThinkPads with 1400x900 in a 12" diagonal. Unfortunately X100, X300, T400 and T500 all offer weaker pixel densities, and 16:9 aspect ratio is not helping.
There is hope on the horizon - ThinkPad Helix advertises 1920x1080 in an 11.6" diagonal, so it is possible that respectable resolutions will make a comeback in future ThinkPads.
Traditional ThinkPad keyboards are my second favorite keyboard to type on after Das Keyboard with CherryMX Blue mechanical switches. The keyboards on ThinkPads offer just the right balance between softness and tactile feedback. I don't have much experience with other brands but the ones I did use were generally stiffer.
Another important ThinkPad feature is keyboard layout, namely the fact that for the longest time ThinkPads retained grouped into fours functional keys and complete Insert-Delete-Home-End-Page Up-Page Down block. X200 is the last laptop with the full keyboard; X220 combines Insert and Delete into a giant Delete key which I personally despise, and X230 uses the "island" design which botches the functional keys and Insert etc. cluster entirely.
Some people love them, some people hate them. I find that I am more precise with the trackpoint, and using it requires less finger movement. To my knowledge only Dell and IBM/Lenovo laptops had trackpoints, probably due to patent issues, and Dell laptops have keyboards that are too stiff and don't work with free software.
Free software support
ThinkPads generally have excellent free software support for the hardware that they include. I have had FreeBSD running on a T30, and more or less every generation since, something I cannot say about Dell hardware.
Last but not least, because there have been so many ThinkPads made, they can be obtained for very cheap nowadays. I recently collected a T61 for $100, a T500 for $100 and an X200 for $150. Yes, they are not exactly cutting edge, but aside from gaming Core 2 Duo is still a very usable chip. Naturally at these price points the screens are the lowest resolution possible, to the tune of 1280x800 in a 15" diagonal on the T61.
At these prices I have been generally converting what used to be towers and servers to ThinkPads. A ThinkPad with its screen off draws on the order of 35 W from the outlet, as measured by a Kill-A-Watt. They are nearly silent and don't produce much heat, perfect for living with.