Yes, PreSonus Studio One 3 Prime is free-- the previous version was called Studio One 2 Free-- and there are versions for both Mac and Windows computers. It's great for a free DAW, although (sadly) it doesn't allow SysEx messages-- if you import a MIDI file or record an incoming MIDI data stream, any SysEx messages will be filtered out (and there's no way to stop that from happening), and you can't add SysEx messages in the MIDI editor.
Some of the other commercial DAWs don't allow SysEx messages, either-- e.g., my favorite go-to DAW is Acoustica Mixcraft, but it doesn't allow SysEx messages, either, although someone on another forum who also uses Mixcraft said he was told by an Acoustica customer service rep that SysEx capability is supposed to be coming in a future version, so here's hoping that's correct! Mixcraft is very easy to use, especially when it comes to layering two or more sounds together or splitting a keyboard between two or more sounds, and the 64-bit version can run both 32-bit and 64-bit plugins without having to install an external bridge utility, since it has one built in. Also, version 7 of Mixcraft has a Performance Panel for launching clips as with Ableton Live (which is another DAW that doesn't allow SysEx messages).
So if SysEx is something you can't do without, be sure to check whichever DAWs you're considering for that particular capability. Cakewalk SONAR allows SysEx, but I have mixed feelings about the way SONAR handles SysEx messages-- specifically, all of the SysEx messages are collected together and are automatically transmitted at the beginning of a MIDI data stream, even if they're supposed to occur at specific times during the stream, so if that's the case then you must manually specify where (or when) in the stream a specific group of SysEx messages should be sent.
Steinberg Cubase also allows SysEx messages, and would be a good choice if you're using a Yamaha keyboard, since Yamaha owns Steinberg, and Cubase has built-in support for Yamaha's SysEx messages and XG features. I'm not fond of the fact that Cubase requires a dongle-- which must be purchased separately-- but fortunately the least-expensive versions (Cubase LE, AI, and Elements) don't require a dongle.
Tracktion is another DAW that allows SysEx messages. The T4 version is free, and the paid versions-- T5, T6, and T7-- are inexpensive. I have T4 through T7, although I haven't come to grips with them yet-- that's actually part of my project for today, in connection with something I'm working on.
Cockos REAPER also allows SysEx messages. It isn't free, although it's also very affordable, and the demo version is full-featured, uncrippled, and never expires-- which is probably a large part of why it's so incredibly popular among a lot of home recording enthusiasts.
There are many other options-- with or without SysEx-handling abilities-- so I won't try to list them all, but they include Avid Pro Tools (which has a free version called Pro Tools First), Bitwig Studio (which also has a clip-launching grid like Live and Mixcraft), Sony ACID (which has a free version called ACID Xpress), and Anvil Studio (the core program is free but there are add-ons which must be purchased).
