Call me paranoid but it took me half an hour to set it up and the monthly fees for the servers are very very low.
Might want to think through whether that really counts as "your own". Who's got hypervisor access to the hardware? Any keys or passphrases that ever hit the disk or memory on someone else's hardware should (at least at some levels of paranoia) be considered "possibly compromised".
(I store "sensitive stuff" on AWS/DigitalOcean/other-vps-providers, but only if it's first encrypted locally and the key/passphrase never gets used/stored on the vps. EncFS works pretty well dealing with that for me... I do, though, "trust" 1Passwords datafile encryption enough to take advantage of the iOS/MacOSX sync features they've implemented over Dropbox. That's possibly not achoice I'd make i I thought I were a target of someone like the NSA.)
For lesser security critical logins, I've got my password software (1Password) on my phone (and iPad). For some intermediate level logins, I need my phone or iPad anyway, I've got TOTP two favor auth (using Google's Authenticator app) on a bunch of important stuff (Amazon/AWS, DigitalOcean, Dropbox, Guthub, the email account that all my domain names are registered with and to which password resets go, and a few other things…)
I've had a "primary computer" stolen before – and I don't intend to ever have that much grief if (when?) it happens again. I'm confident that even if all the electronics from either one of my work or home get stolen, I could be back into fully productive work-mode in half a day and one maxed-out-creditcard at the local Apple store. (If someone hits both my work and home locations simultanously, I suspect I've got bigger problems that whether I'll have angry clients shouting at me before the weekend…)
But if I do need to, I have 1Password on my phone as well and can get the passwords from it.
But I would not really be comfortable using it on an unknown computer, unless I had good knowledge that it was properly administered.