100%. Many companies "Pivot" and when they do, they let their current users know that the service is shutting down - but that they're now moving onto something new (or launching a new company).
Flowtown (my last company) did this 3 times. We even leveraged users to test the new product before we made it public.
Just be respectful of peoples time/email and only send to them if they opted in to receive company updates.
What's the time differential? If it's a logical next step, it's probably ok. If it's a complete shut down - or an asset sale (which would mean that the email list is owned by the acquiring company) - or longer than say 4-6 months, I would say no.
That being said, if you are in the process of shutting down the first company, there is nothing wrong to asking your users if they are open to hearing more in the future.
If your new thing would be of value to your subscribers - then sure.
Let them know "WIIFM?" in language that makes sense to THEM (in other words - use good marketing).
Assuming the product/service + the message + the offer is a good fit it won't be considered spam. Give them a chance and a good reason to opt in to a new list for your new project. And remember to monitor your stats (open rates and CTR).
Let me know if I can help in any way.
Best of luck on your new venture!
An attitude towards 'failure' is very important and often determines how the society accepts innovation all together... In many successful places failure is like a shevron of experience - and that's how it should be. So you are much better off after your first startup failed.
But if you know that your audience is seeing it differently, then better not to approach them right away. Otherwise you will be caught in discussions 'how is this one is better than that other one'... And this is a waste of time:(
Some great tips above. Those who have followed me for a while online have witnessed many ideas I have began to develop and then tossed by the wayside. Many domain names and Twitter accounts archived or deleted. There is no problem with transitioning your previous customers to your new venture. You just want to be careful that you do nothing that asks to much of them or creates any confusion. If your previous subscribers were paid, I would suggest offering them some sort of a discount. If there is anything overlapping, don't ask them to pay again. Give them 2.0 for free.