CargandoLeches is a webapp that lets you load games in any Spectrum model 15-20x faster. No tape is needed, but a digital audio source, as the PC sound card, CD player, MP3, etc. It might work with actual tapes using lower speed settings.
No hardware mod is needed, but you may need a firmware mod. Modified ROM's are available in the download section. You will need some kind of flash/EPROM memory, a programmer and posibly, an EPROM eraser. Electronic device shops may have a programming service available to customers.
Worst case, if you cannot modify your firmware, but have access to a +2A/+3 class machine, CargandoLeches benefits can be enjoyed, as these computers feature a paging scheme in which RAM can be used at ROM addresses. The inconvenient is that the machine would work as a 48K machine, this disallowing full 128K game loading.
The best part of it is that special loaders and/or special loading procedures are not needed. TAP and SNA files work off the shelf. TAP files load transparently, even if it is a multiload game.
Old-fashioned tapes do also work. The new ROM detects the loading method and reverts to the original ROM code if needed. This is handled transparently, with no user or program intervention.
The online player has two playing options: online conversion and playing, which allows to instantly play a file from within the browser (supported in HTML5 aware browsers, such as Chrome and Firefox), or online conversion to a WAV file for later playing. Both methods generate a stereo audio signal, with one channel being the inverted version of the other one, so the voltage seen by the computer is twice the original and the loading process less prone to errors. To use this feature, you have to build an audio cable with a 3.5mm stereo jack at one end. The wires will be connected to both L and R at this jack, leaving GND unconnected. The other end will have a 3.5mm mono jack: one of the wires from the stereo jack will go to the tip, and the other one to the GND portion.
If using such connection, it's advisable that the player should not use a grounded power cable if the Spectrum or the monitor already have one. Failure to observe this will cause that one of the channels to be shorted to GND the moment that the audio cable is connected between the Spectrum and the player, possibly causing damage to the player. If in doubt, use a stereo jack to 2-mono jacks cable, and use at the Spectrum the mono jack that is connected to the L channel.
In this video you can see a working ultraload in a spectrum 48K in less than 20 seconds: