Are you by chance using the server? I had horrible lag when I switched from the Bukkit (R.I.P. you beautiful Bukkit), back to the actual server. Turned out that the GUI overlay borks the snot out of the CPU, and causes everything to lag and be jerky.
Slow minecarts appears to be due to server lag; I've noticed this myself in 1.6.x near my base at night when a bunch of zombies try to pathfind to the villagers in it; the minecart would start moving in a stop-and-go fashion, more or less in time with the jerky movement of the stars and sun/moon (luckily, I found a patch that virtually eliminates this lag unless I spawn dozens of zombies then go on a pillar and switch to Survival, otherwise, I don't get any lag in minecarts, though riding horses into new chunks has some lag).
It is also worth noting that server lag is a cause of a problem with boats; in this case, boat movement is only controlled client-side (see this reply), which means that server lag doesn't visually affect movement but the server can fall behind, with strange results like exiting a boat far from where you appeared to be (I've even heard of cases when you fall into unloaded chunks, though I myself haven't had any of the issues (not tested in 1.8), probably because I don't use boats to explore new areas, only in existing areas, and don't go that far).
Yes but the super fast minecarts were in fact so fast they flew off the rails on corners killing everyone inside. OSHA (Occupational safety and health Administration made them put back the old slow ones.
Has anyone found out how to fix the slowness problem? My horses are moving incredibly slow (recently)... I tried taming several to see if it was just a bug with a certain type but all seem to be moving slow - and like someone else said they can move "fast" up hill (at times)... Somewhat frustrating now to be honest, but haven't found an answer so far... tried everything suggested in all forums so far lol.