If you played Morrowind. You know how it has those Propylon Chambers and those items that transports you to various locations when you put them on? So if you are playing as a Mage you can role-play that after sometime. You learned a spell that teleports you to your location(fast travel). To keep it inline you can only do it so many times a day/week.

For non-mages you can role-play that you found an item like a necklace that has the ability to teleport you to your location(fast travel). To keep it inline you can only use it so many times a day/week.

Well having a magic that teleports you over vast distances, that won't take away from the RP experience and is a very good way to explain the fast travel. I guess you can always pretend you have one of those abilities if you want to anyway.

There are several reasons. I personally dont feel it's right to just pop up somewhere unexplained. I feel i should either pay for a transportation service or have a magical ability that allows me to, like Morrowind's Mark and Recall spell. Even the new Bat Travel mod for Dawnguard is ok in my book because I would have to be a Vampire Lord to use the ability.

Also even though you have traveled there once, there is so much you could have missed, not to mention Skyrim has radiant quests that can pop up anywhere. For example i was taking a shortcut that i sometimes take through the wood when I looked to my left and saw a shack I had never noticed before. There was a few little things that were interesting there. If I had fast traveled I would have probably never discovered it.

I don't fast travel on my characters, but I RP teleportation magic on my Mage by casting a high level spell and then fast travelling to the nearest town.

I fast travelled a lot with my first character, but then I discovered how much I missed by doing that.
The random encounters - sure, most of them are the same one frequently occurring (though I noted that different random encounters seem to be frequently occurring on different playthroughs), but after at least 400 hours with my previous characters, I've already experienced three random encounters I've never had before with my new character - and I know that there are a few I still haven't seen.
All the unmarked locations and easter eggs - I've never would have found Excalibur, three billy goats, or the necromancer who practises on chickens if I had kept on fast travelling.
The beauty of the landscape, how my plans get changed when I run into some enemies, all marked locations I never would have discovered...

When I was about to retire my first character, I just wanted to finish the main quest and a few sidequest, and then I started fast travelling everywhere again. And I was almost immediately bored. I no longer felt for my character the same way, and everything felt rushed.

So now I walk (or rather, run - I don't have time to actually walk everywhere) most of the time. When I don't feel like walking the same distance for the umpteenth time, or don't have time for walking I use a carriage - it feels a little better than simply fast travel. Basically, I only fast travel when I've lost a follower or something like that. For me, that's the way I like to play. Sure, I could level faster and get through questlines faster if I kept on fast travelling, but I'm pretty sure that if I did, I would have grown tired of Skyrim a long time ago.