I'm exploring safe places to store my startup's intellectual property. These could be anything from vendor lists to investor term sheets, etc.
Should I trust cloud service providers like Google and Dropbox with such material? If not, what are some alternatives that I can look into?
As with any service or way of storage, it'll never be 100% secure..
All these companies have to abide with the data protection act, of which one rule states "All Data must be held securely" so you can rest assure that these companies - especially the big ones like you've listed - will hold your data securely. Also, look at the sheer size of the two companies, issues such as downtime and hacking is very, very minute (if any).
Look at the practicality and accessibility issues at hand here, weigh them up with the cons you see in these businesses and go from there.
Personally however, I see no issues as to why it wouldn't be an ideal place to store your documents.
An alternative to using public services like Google Docs is hosting an OwnCloud instance on your own server. That way you are in full control.
The downside to OwnCloud: another thing to manage if things break. And more often than not, it's easier to screw up the security (or backups) by hosting it yourself.