Assume I have a traditional IRA, which I had previously rolled my 401(k) into. I now would like to transfer to another traditional IRA at another broker (Vanguard). Are there any tax implications to this, or will it simply be moving the finds from one IRA to another?
No issue. You are permitted to move like accounts (i.e traditional to traditional or Roth to Roth) directly with no tax issue. Problems can arise when taking possession of the funds in a 60 day rollover or when moving from traditional to Roth, the latter being a taxable event.
A comment from @Dilip_Sarwate is an important one and should be part of my answer -
Perhaps it is worthwhile to add that newly changed rules limit 60-day rollovers to one per year overall. It is no longer permissible to do a 60-day rollover from, say, one's Fidelity IRA to one's Vanguard IRA and also a 60-day rollover from one's ScottTrade IRA to one's Schwab IRA in quick succession; the money received from ScottTrade would be treated as a distribution, and any money deposited into the Schwab IRA (even if within the 60-day period) would be regarded as a new contribution, not as a rollover, and thus be subject to excess contribution rules etc.