Since I've noticed quite a lot of interest in low-level stuff from the community recently, especially on IRC when it comes to reversing/exploit dev, below you'll find some pwning/reversing challenges that I've enjoyed playing over the past months.
Note: I won't be referring to the ones everyone is talking about ( i.e overthewire, smashthestack etc ) since they are kinda getting "old" in my opinion.
HackCenter - These challenges are hosted by CMU (Carnegie Mellon University). I highly recommend those. Here's one of the many reasons.
LSE CTF - @IoTh1nkN0t and I have been playing around with the 'crackmes' category of that website. They are quite decent and the difficulty level increases quite fast. They've got pwning/shellcode/web/crypto/forensics as well.
microcorruption - Really fun reversing challenges with an exceptional GUI. It gets you in the process of researching since the "binaries" are using a different ISA from the one you're probably used to.
pwnable.tw / pwnable.kr - I think the title says it all.
picoCTF - Not sure if @0x00pf has anything to do with it . Either way, these challenges are at the level of high school CTFs and they are highly recommended for CTF beginners. I believe they are hosted by PPP. If you don't know PPP, you should definitely google them.
RPISEC - This is an open course on Modern Binary Exploitation with lectures slides and quite a lot of reversing/pwning challenges.
protostar - From basic to slightly intermediate exploit dev challenges with source code provided for each level. If you are stuck with any of the challenges, you should 100% check out LiveOverflow on youtube.
Oh well, I think these are more than enough for now. If you've got more suggestions, feel free to let us know in the comment section.