I always take my own container to the butcher's shop - this caused some confusion at first and I had to be VERY firm that I didn't want a piece of plastic lining my glass container. Now the local butcher is used to me and my 'saving the planet ways' and my request usually generates some environmental discussion or chit chat, either with the staff or with other customers.
If you haven't got a butcher's shop close at hand, or if you don't eat meat, then you can still take along your own container to a deli counter in a supermarket or in an independent store, for; fish, cheese, roasted vegetables, salads etc.
I favour IKEA's range of glass containers with plastic, clip on lids, called IKEA 365+ - they come in different depths yet use the same lids, so no more lid-confusion! They are easy to keep clean, can be frozen and the glass part can be put into the oven and / or used to serve straight to the table. Voila!