As I look at the Megathread, Porn thread and other picture threads, I see a lot of folks still prefer toe straps & cages. Besides economics, is there a reason to use these types of pedals as opposed to going clipless?

Other than the ability to use regular shoes, not really.

Some vintage riders think that toeclips are more "original/retro/classic".

SPD and other 2-bolt style pedals/cleats can support shoes that are walkable, although I still like to change shoes if I'm doing something for a few hours.

One can use cleats with toeclips, but I think most people use them today with just street shoes. They work well, but aren't quite as secure as clipless, suffer from flex with whatever sole the shoes have, and don't hold the feet quite as stable.

Plastic toeclips don't damage the shoes as much as metal ones.

I ride clipless on the road for sport. But for commuting/utility riding I use clips and straps so I can wear normal shoes and get around easier in stores and such.

It's not a question of one being better or worse, but of being more suited to the particular application.

I also stick to clips and straps on my fixed wheel bike because it only has a front brake and I'm concerned about unexpected release of a clipless pedal if/when I reverse torque hard.

I ride clipless and straps/cages. Really just depends on how I'm feeling that day. Skidding/slowing down feels really weird on cages because your foot feels like it's gonna slip out and the power transfer isn't really there without clipless. I feel a bit more tired when I'm riding with straps/cages than I do clipless because of the extra effort required.

All of my road bikes, regardless of drivetrain flavor, use Look clipless pedals while the town bike uses toeclips & straps.
Fitting pedal types follows function.

-Bandera

Long rides & direct commutes of reasonable distance = clipless

Commute that involves a lot of walking or standing = clips & straps

Personally, I'm not very fond of sneaker based SPD shoes that are marketed as "walkable". They should market them as anti-slip if anything.
Compromises for your feet where if they awesome to walk in, they suck at pedaling and vice-versa.

If I'm going out for the sole purpose of a ride, planning on spending more time on the bike than off, clipless it is. After about 10 miles, I start to get numb toes if I'm wearing my regular sneakers.

This. And unless you use slotted cleats with your clips and straps, clipless pedals will give more secure foot retention.

I learned to skid with clipless pedals (Shimano M520) and for the longest time loved them because I couldn't figure out how to keep my feet from slipping out of the toe clipped/straps. Then I somehow got it my head that I simply had to learn to ride/skid with clips/straps. So I did. Now whenever I use clipless pedals I always seem to turn my foot at the wrong time, usually when skidding, and my foot comes "unclipped." Ironic, huh? Therefore, I just stick with clips/straps because it's easier for me, feels more secure, and I don't have to haul around a pair of regular shoes everywhere. Having said that, I still use clipless pedals (Look) on my road bike.

To answer your question: There is no real reason to use one over the other aside from personal preference.

All I have ever used is Shimano M520 clipless. Never tried straps or cages. Transitioned over from mountain biking and never looked back.

For long club or t-shirt rides - cleats.
10 mile commute with stoplights or around town - cages.

Bare spindles for me.

That was my issue. On longer ride my toes would go numb and actually stay numb even hours after finishing the ride.

Having stiffer soled shoes makes a big difference using straps. The problem is that all of my stiff soled shoes were expensive low top hiking shoes (Vasque, Salomon)...after a few weeks of riding, the straps would start to wear holes in my shoes which isn't exactly a good thing if you're hiking in the rain. I tried to go riding with soft soled canvas/suede casual shoes and my arches would just ache on any type of ride over 30 minutes.

I bit the bullet and went to clipless combined with ultra stiff road shoes (My Shimano's are carbon soled). Everything improved: no numbness, no arch pain, felt like I was getting more power into the pedals, etc... Only downside was walking.

I could see switching back to straps if I'm doing a 10-15 min ride to a friend's house and don't want to switch out shoes...but everything else, you really can't beat clipless.

I bought my black Shimano 170's for around $65 brand new...which are basically the top of the line buckle/carbon soled model from last year. Just wait for sales (this shoes but last years model SH-R171 - ROAD - CYCLING FOOTWEAR AND PEDALS - LIFESTYLE GEAR - SHIMANO )

On longer rides they cannot be beat.

"Yabba-dabba-doo"

I had switched back to SS and platforms for the winter but I'm getting the itch to ride FG already, hence the question. I am thinking of installing the cages and using my insulated hiking boots.

What about those single strap setups like Fyxation? Any good?

It's been claimed that the metal cleats of clipless transfer heat from the foot. In my experience it's true.

ftw

Aerolite pedals, the next best thing to bare spindles (the cleats aren't fun to walk on, though):

If you ride fix gear very fast downhill. good toeclips, straps and cleats give you the security of knowing that even if cleat releases, your feet are still on the pedals. I find that at pedal RPMs over 175 I have a hard time being aware of whether I am keeping my feet straight (especially when I am offsetting my weight for a turn. (Cars have told me I was going 45 when I was riding a 44-17, 215 RPM. Years ago, I used to go a lot faster on a 42-17.)

Toestraps pulled tight give you the freedom to ride and never think about your pedals, no matter how fast or hairy the going gets. (You do have to remember to loosen them before stopping, but the worst that can happen is you fall over at very low speed, not have your ankle struck by a heavily weighted hammer swinging at 200 RPM. That "hammer" isn't light. It effectively weighs you + the bike times the gear ratio you are riding times the difference between your wheel radius and your crank length. Say 150 lb rider + 20 lb bike X 42/17 X (27/2)/7 = 810 lbs. Makes a sledge hammer look like a toy.)

Edit: Exustar maks a good road cleat for quill/rattrap pedals. They call it a track cleat, but it is what we would have used 40 years ago before clipless had modern shoes with bolted cleats existed then. They require the LOOK three bolt shoes (although they only use the rear two bolts). Cost is about $20. These are very high quality cleats. Don't get the $75 model. THose are track specific and for the incredibly strong sprinters who care far more about having a cleat that will reisit the hardest pull up than whether they can actually get their foot out when they stop. (They always have a rail they can pull up to grab.) If they won the race but it take 5 minutes to get their foot out, cool! The cleats worked! Obviously not what you want in traffic.

Ben

Fly Pedals - Universal Clipless Pedal Adapter

The only problem i see with those is that you have to take them everywhere with you since they can just be snapped out of the pedal

The Fyxation ones actually kinda suck but better versions of that type of setup (velcro straps and platform pedals) like YNOT and Holdfasts are a great choice.

I had the Holdfasts and they were fine but the nylon trim wore out pretty quickly. I put Fyxations on my next build thinking they were all pretty much the same but the Fyxations weren't as stiff and tended to sag and crush and stay crushed if you didn't get your foot in and quickly became frustrating. YNOTs are the best of the lot as they are stiff and hold open well so your feet slide right in first time. After several years they still look new and haven't worn or have retained this stiffness.

Advantages of this setup are easy adjustment for variety of shoes. No clips to increase toe overlap, nothing to scuff your shoes as metal clips can do and the pressure point is spread over your a larger area of your foot . Combined with a wide platform it makes for a very comfortable and secure feeling solution, second only to clipless for me (have ridden both single and double straps and prefer these). On my road bike I ride clipless (Shimano Deore XT smooth).

Your milage may vary.

I don't see how this would be a better solution than just switching to platform pedals, which would cost less and take about 20 seconds.