My first (AM) DX...
I had gotten a free portable sports radio with a bicycle I got about 18 years or so ago. Naturally it had analog (dial) tuning, poor sensitivity and even worse selectivity, being a freebie.
I was tuning around one night with it before I went to bed, and I heard this extremely faint talk station a little bit below a religious station I knew was on 910, and above a spanish station on 860. My dad & I tuned it in in the car - and it was 890AM KDXU from St George, Utah. (Obviously the signal was much better on the car radio.)
As for FM... I haven't really gotten anything of significance -- often I can pull in 103.3 and 97.3 Santa Barbara, CA from some of the higher hills near El Cajon / La Mesa, CA, but considering the fact that some of you regularly probably receive stations from much farther away, my FM "DX" is really considered local "right under the stick" to you all.

It probably also doesn't help that I happen to be stuck with an FM radio with absolutely horrendous selectivity - for example, I am completely unable to pull in a station on one channel that is let's say -90dBu (or whatever is considered an extremely weak barely listenable signal on a good quality FM radio - maybe one about 150 miles away with a 1kW transmitter) when I am within 1/8 mile of a local 100kW stick 0.2MHz away (or maybe +150dBm or something - not sure either).
Also my AM DX ability or lack thereof is bad too - for example sitting at Highway 52 and Mast Blvd in Santee, CA, I absolutely have no trace of WSM Atlanta in the daytime (or at night for that matter) or WJR Detroit at any time - my radios are not selective, sensitive or directional enough.
I don't do TV.