I do, and let me explain why.
I would love to not have to charge for samples but, the reality is that it is simply not financially feasible, especially with handmade and bespoke work.
Here's what goes into a sample that you receive from a bespoke handmade stationer:
time spent sourcing materials for bespoke work;
cost of card, adhesive, embellishments;
time spent type-setting wording;
cost of printing;
time to make up samples and any variations;
cost of posting the sample to you.
When making wedding stationery, I batch the individual processes to maximise time but, with a sample, I have to go through every process once and this can amount to the equivalent of a full day's work in some cases.
Instead of offering free samples, I offer a free in-person or online consultation, where I will bring along/show you examples of work and talk to you about your special day to get a feel of whether or not what you're looking for is something I'll be able to make for you. We also discuss budget and the decisions you can make to get your perfect stationery within that budget. You get to see the quality of my work and can decide if you think you can work with me and all it has cost each of us is a short meeting. After that discussion I can make up samples but, I will charge for them. However, this cost is redeemable against your wedding stationery when you book as I won't have to re-invent the wheel. Equally, should you decide not to go ahead, you get some personalised stationery and I have been paid for my time and covered the cost of materials - we both win!
Having said all that, you still need to shop for ideas, right? A great way to do this is to create a mood board on Pinterest - it costs nothing to collate images of the types of stationery you like - and you can then take that along to a consultation/send it to prospective stationers to give them an idea of the look you are going for. However, please remember that any professional stationer won't copy anyone else's work :)