Setting an SPF record for all subdomains of my domain

Is this possible? Like a wildcard TXT record of some sort?

Yes, it is possible to define a wildcard TXT record.

Notice that you should define both a TXT RR and a SPF RR. Update: This answer was originally made in 2011. At the time SPF RR was a thing. However, according to RFC7208 the use of SPF RR has been discontinued and SPF content should only be published in TXT records.

Example
In my home I run a local DNS server with the .fbh domain extension, I have created this record:

*.email         IN  TXT "v=spf1 mx -all exp=bad.example.com"

And this gives me the same response for all queries to *.email.fbh:

$ dig +short TXT test.email.fbh
"v=spf1 mx -all exp=bad.example.com"

$ dig +short TXT smth.email.fbh
"v=spf1 mx -all exp=bad.example.com"

You can, however, include a central spf record in the invidual subdomain spf records.

Each individual spf records for the subdomains could look like this:

v=spf1 include:_spf.domain.tld ~all

And then add a TXT record for _spf.domain.tld with the actual spf values:

v=spf1 ip4:1.2.3.4/30 200.298.100.1/24 ~all

This way, you only need to maintain _spf.domain.tld, and not the records for the individual subdomains