Do X.25/Frame Relay/ATM/MPLS have their own switches?

There were, in fact, dedicated X.25 hardware switches produced by the likes of BBN (and others) in the late 70's and into the 80's. Pictures of this sort of thing would be the domain of various museums out there, as dedicated X.25 switches were retired by the early 90's (nb - obviously some amount of this stuff probably persisted in some dusty corner, likely to this day).

In practice X.25 and Frame Relay services grew and were extended in the 90's via the early generations of carrier-oriented ATM switches (Stratacom, Cascade, Fore, etc), which actually provided these protocols as part of their offerings. In later generations ATM switches were also the platform upon which the first MPLS switching was developed, originally as a way for packet switched networks to natively utilize ATM services.

Concurrent with the later generations of these ATM switches, routers (..particularly by the late 90's into 2000) began to get much faster and denser and supported switching of these technologies both natively and via various encapsulations/overlays. It's probably safe to say the routers (or, more properly, packet switching) won and now both IP and MPLS are handled on common hardware platforms (i.e. routers).

Historically, Frame and ATM used purpose built devices. X.25 is a bit before my time, so I don't know if anyone had hardware switches for it. Today, almost everything is done with "soft switch" gear -- i.e. software. A Cisco IOS router can be configured to perform frame-relay, atm, and x.25 switching.

MPLS is functionally just a fancy [simpler, faster] way of routing, and that's how manufacturers have dealt with it. While larger iron may have hardware support for MPLS (like they do for IPv4, IPv6, ethernet switching, routing, etc.), it's not an independent layer-2 protocol.