with higher cost items (usually vehicles, large appliances and electronics) i'll anonymously research ahead of time if a particular store/company takes our reward type credit cards and if there's a cap on it so I know where I stand before I start negotiations. that way I can use the cards BUT I can also use it as a final negotiation point and ask if they will give me an even further discount if I opt NOT to use my credit card. I've found many retailers who will take the amount down to match what they will save in merchant transaction fees, and since that also additionally brings down the taxes on it I end up ahead of what I would reap in reward points or cash back rewards. I recently did this with a purchase that was best priced at about $6800 before sales tax. b/c the business was willing to drop their price by the amount of their merchant fee (3%) I ended up saving (between price and tax) about $225. a 1% or 2% reward on the best negotiated price using a credit card would have only netted me about $75-$150. I would rather have the extra money in pocket.
with some purchases though i'll only go to a place that accepts american express b/c of american express's extended warranty coverage (doesn't extend to vehicles) but when we purchased our car we used the costco program which my research showed was absolutely the lowest price we could get so I didn't care that the dealer capped the amount so I still got a small reward back plus the service and parts gift certificates costco sends for using the program.