I got thrilled with chasing DX as a Novice in 1976.  The though of my radio waves being heard by another ham thousands of miles away really thrilled me and I chased DX stations for years.  I have a DXCC certificate issued on April 10, 1978 (and 6 months of that was some back-and-forth "Discussion" with the ARRL) for 100 countries.  I never bothered submitting any additional countries and when I shut things down about 20 years ago I had 235 countries worked.

Fast forward about 20 years to February of this year and I got back on the air.  With all the changes in equipment and procedures I decided that I was going to start from scratch with a new "Electronic" DXCC.  I worked a bunch during the CQ Worldwide RTTY contest the second weekend of February.  I then talked with a friend who is on the DXCC Honor Roll (338 of 340 countries confirmed) and he recommended FT8 as a great place to work DX.  I tried it and he was right, the DX is most assuredly there.  So instead of the 2 years it took the first time I gave myself 2 months to confirm 100 countries which I thought was very pessimistic.  I just couldn't see it happening since that's 12.5 new countries a week for 8 weeks.  I got close though.  Between February 3 and April 3 I worked 102 countries but I only had 92 confirmed.  The 100th confirmation came through on April 12.  Right now I have 112 worked and 105 confirmed and still climbing.  I caught Algeria yesterday.

The majority of them are the easy countries that are seen every day but there are also some really nice "Nuggets" of DX sprinkled in there to.  In fact there were 4 countries that I had never worked before (Bonaire Island (PJ4), Indonesia (YB8), Oman (A4), and Western Malaysia (9M2)).  There might have been 1 or 2 caught in the Extra portions of the bands but the vast majority were in the General portion of the bands.  The vast majority were on 20 meters with a few on 80, 40, and 15 but none on 10 meters.  My only antenna is a 6-band trap vertical, so no huge beam to help out.  I do have a 600 watt amp but didn't use it for most of them since I sort of wanted it to be "Barefoot Only" (although I admit that when it looked like I was going to miss out on a few I really wanted I did flip the switch.

The point isn't to brag about an accomplishment but to point out that you don't need an Extra class license or a big antenna or a legal-limit amplifier to work DX.  It's there, even with the marginal propagation conditions and the lack of DXpeditions we have now,  and it can be worked with a 100 watt station and a moderate antenna system.  My friend that I mentioned above worked his original DXCC on that little 200 kHz section of 10 meters where Technician class licensees are allowed to use SSB, and even though he's on the DXCC Honor Roll he only holds a General class license now.  So get out there and do it!  Learn to use what you have even though you might have to be sneaky about it.  If there is a pileup know that you can't work through it but also be aware that they are making so much noise that the DX station is going to have a hard time hearing one callsign in the QRM so wait a few seconds.  They will all send at the same time and then stop to see if he is calling them.  THAT point is when you want to send your call, while they are quiet.  Know how propagation works.  If he isn't hearing anybody in your call district then odds are he won't hear you so don't be discouraged by it.  Also know when conditions will be best in your part of the world.  It may be late at night or early morning but we've all lost a lot of sleep chasing these elusive stations.  I promise, I absolutely promise, the first time you work that super-rare island in the middle of nowhere that it's all worth it.  My first one was 4 days after I got my General license.  I worked "Father Dave" (CE0AE) on Easter Island and I was hooked from that day forward.

So get out there and do it.  Virtually all of you have a station capable of getting through to anywhere on the planet so do it.  Print a copy of the Official ARRL Countries List so you know who you are hearing (although there are a lot of prefixes that don't match up) and go for it.  I guarantee there is someone here who can beat my two months and I want to see you do it.  It's not hard and it is a lot of fun so who is going to man up and take on my challenge?  Post a note here with your start date and edit it for your milestones (i.e. 25, 50, 75, 100, etc.).  Keep in mind that technically I didn't make it since I didn't have 100 confirmed at 2 months, so really it's wide open.

Very much this, but you do have to be aware that it is sunspot-cycle dependent.

Sometimes they fall into your lap, and sometimes you have to work for weeks or months to snag them.

One of my hardest ones was 9N1MM. I chased him for a long time, and I never did get Pitcairn Island, as I could never get through the pileups. I used to hear them often.

(100W to a dipole at ~35')

Couldn't agree more.  I literally just turned my radio on yesterday afternoon, switched over to FT4 on 20 meters (14.080) and the first thing I saw was a CQ call from 7X3WPL in Algeria.  I pounced on it and got him before the pileup started, it must have been his first CQ call ;)  That was one that fell into my lap.  The list of those I've chased and missed is long and illustrious but I don't think I've ever heard a station from Nepal.

I do have Pitcairn Island from 1993.  That place has an interesting history.  If you aren't familiar with it, Google it.  I've gotten some gorgeous QSL cards from islands in the Pacific.  They really make me want to buy a boat and just sail around for a few years ;)

And you are also absolutely right about solar conditions.  We are in the doldrums now and propagation is really weak.  I was a ham during Cycle 21 which was supposed to be the best one ever, and it was wild.  I used to sit at home late at night and chat with some local friends with the power run back to about 25 or 50 watts and we would have people from all over the world drop in to say hello.  There was one guy from New Zealand that came by every few days just to say hello and he was as clear as talking over a 2 meter repeater.  100 watts was overkill at some times and I was running a kilowatt into a 2 element quad.  S9 +20 in Australia was commonplace, and I put my amp into standby for Europe or South America.  Those were the days ;)  I hope I live to see them again!